Dune Core Modules (2.8.0)

rannacherturek3dlocalbasis.hh
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_RANNACHER_TUREK_3D_LOCALBASIS_HH
4#define DUNE_RANNACHER_TUREK_3D_LOCALBASIS_HH
5
6#include <numeric>
7#include <vector>
8
11
12#include <dune/localfunctions/common/localbasis.hh>
13
14namespace Dune
15{
16
17 template< class D, class R >
18 class RannacherTurek3DLocalBasis
19 {
20 static const int coefficients[ 6 ][ 6 ];
21
22 public:
23 typedef LocalBasisTraits< D, 3, FieldVector< D, 3 >,
24 R, 1, FieldVector< R, 1 >,
25 FieldMatrix< R, 1, 3 > > Traits;
26
28 unsigned int size () const
29 {
30 return 6;
31 }
32
34 inline void evaluateFunction ( const typename Traits::DomainType &in,
35 std::vector< typename Traits::RangeType > &out ) const
36 {
37 typedef typename Traits::RangeFieldType RangeFieldType;
38 RangeFieldType y[ 6 ] = { 1, in[ 0 ], in[ 1 ], in[ 2 ],
39 in[ 0 ]*in[ 0 ] - in[ 1 ]*in[ 1 ],
40 in[ 1 ]*in[ 1 ] - in[ 2 ]*in[ 2 ] };
41 out.resize( size() );
42 for( unsigned int i = 0; i < size(); ++i )
43 {
44 out[ i ] = RangeFieldType( 0 );
45 for( unsigned int j = 0; j < 6; ++j )
46 out[ i ] += coefficients[ i ][ j ]*y[ j ];
47 out[ i ] /= RangeFieldType( 3 );
48 }
49 }
50
52 inline void evaluateJacobian ( const typename Traits::DomainType &in,
53 std::vector< typename Traits::JacobianType > &out ) const
54 {
55 typedef typename Traits::RangeFieldType RangeFieldType;
56 RangeFieldType y0[ 5 ] = { 1, 0, 0, 2*in[ 0 ], 0 };
57 RangeFieldType y1[ 5 ] = { 0, 1, 0, -2*in[ 1 ], 2*in[ 1 ] };
58 RangeFieldType y2[ 5 ] = { 0, 0, 1, 0, -2*in[ 2 ] };
59
60 out.resize( size() );
61 for( unsigned int i = 0; i < size(); ++i )
62 {
63 out[ i ] = RangeFieldType( 0 );
64 for( unsigned int j = 0; j < 5; ++j )
65 {
66 out[ i ][ 0 ][ 0 ] += coefficients[ i ][ j+1 ]*y0[ j ];
67 out[ i ][ 0 ][ 1 ] += coefficients[ i ][ j+1 ]*y1[ j ];
68 out[ i ][ 0 ][ 2 ] += coefficients[ i ][ j+1 ]*y2[ j ];
69 }
70 out[ i ] /= RangeFieldType( 3 );
71 }
72 }
73
75 void partial (const std::array<unsigned int, 3>& 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 out.resize(size());
84 auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
85
86 using RangeFieldType = typename Traits::RangeFieldType;
87 RangeFieldType y[3][5] = { { 1.0, 0.0, 0.0, 2*in[0], 0.0 },
88 { 0.0, 1.0, 0.0, -2*in[1], 2*in[1] },
89 { 0.0, 0.0, 1.0, 0.0, -2*in[2] } };
90
91 for (std::size_t i = 0; i < size(); ++i) {
92 out[i] = RangeFieldType{0};
93 for (std::size_t j = 0; j < 5; ++j)
94 out[i] += coefficients[i][j+1] * y[direction][j];
95 out[i] /= RangeFieldType{3};
96 }
97 } else {
98 DUNE_THROW(NotImplemented, "Desired derivative order is not implemented");
99 }
100 }
101
103 unsigned int order () const
104 {
105 return 2;
106 }
107 };
108
109
110
111 // RannacherTurek3DLocalBasis::coefficients
112 // ----------------------------------------
113
114 template< class D, class R >
115 const int RannacherTurek3DLocalBasis< D, R >
116 ::coefficients[ 6 ][ 6 ] = {{ 2, -7, 2, 2, 4, 2 },
117 { -1, -1, 2, 2, 4, 2 },
118 { 2, 2, -7, 2, -2, 2 },
119 { -1, 2, -1, 2, -2, 2 },
120 { 2, 2, 2, -7, -2, -4 },
121 { -1, 2, 2, -1, -2, -4 }};
122
123} //namespace Dune
124
125#endif // #ifndef DUNE_RANNACHER_TUREK_3D_LOCALBASIS_HH
Implements a matrix constructed from a given type representing a field and compile-time given number ...
Implements a vector constructed from a given type representing a field and a compile-time given size.
#define DUNE_THROW(E, m)
Definition: exceptions.hh:216
constexpr T accumulate(Range &&range, T value, F &&f)
Accumulate values.
Definition: hybridutilities.hh:289
Dune namespace.
Definition: alignedallocator.hh:11
D DomainType
domain type
Definition: localbasis.hh:43
RF RangeFieldType
Export type for range field.
Definition: localbasis.hh:46
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