Dune Core Modules (2.8.0)

brezzidouglasmarini1simplex2dlocalbasis.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_LOCALFUNCTIONS_BREZZIDOUGLASMARINI1_SIMPLEX2D_LOCALBASIS_HH
4#define DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI1_SIMPLEX2D_LOCALBASIS_HH
5
6#include <array>
7#include <bitset>
8#include <numeric>
9#include <vector>
10
12
13#include "../../common/localbasis.hh"
14
15namespace Dune
16{
26 template<class D, class R>
28 {
29
30 public:
33
36 {
37 for (size_t i=0; i<3; i++)
38 sign_[i] = 1.0;
39 }
40
46 BDM1Simplex2DLocalBasis (std::bitset<3> s)
47 {
48 for (size_t i=0; i<3; i++)
49 sign_[i] = s[i] ? -1.0 : 1.0;
50 }
51
53 unsigned int size () const
54 {
55 return 6;
56 }
57
64 inline void evaluateFunction (const typename Traits::DomainType& in,
65 std::vector<typename Traits::RangeType>& out) const
66 {
67 out.resize(6);
68
69 out[0][0] = sign_[0]*in[0];
70 out[0][1] = sign_[0]*(in[1] - 1.0);
71 out[1][0] = sign_[1]*(in[0] - 1.0);
72 out[1][1] = sign_[1]*in[1];
73 out[2][0] = sign_[2]*in[0];
74 out[2][1] = sign_[2]*in[1];
75 out[3][0] = 3.0*in[0];
76 out[3][1] = 3.0 - 6.0*in[0] - 3.0*in[1];
77 out[4][0] = -3.0 + 3.0*in[0] + 6.0*in[1];
78 out[4][1] = -3.0*in[1];
79 out[5][0] = -3.0*in[0];
80 out[5][1] = 3.0*in[1];
81 }
82
89 inline void evaluateJacobian (const typename Traits::DomainType& in,
90 std::vector<typename Traits::JacobianType>& out) const
91 {
92 out.resize(6);
93
94 out[0][0][0] = sign_[0];
95 out[0][0][1] = 0.0;
96 out[0][1][0] = 0.0;
97 out[0][1][1] = sign_[0];
98
99 out[1][0][0] = sign_[1];
100 out[1][0][1] = 0.0;
101 out[1][1][0] = 0.0;
102 out[1][1][1] = sign_[1];
103
104 out[2][0][0] = sign_[2];
105 out[2][0][1] = 0.0;
106 out[2][1][0] = 0.0;
107 out[2][1][1] = sign_[2];
108
109 out[3][0][0] = 3.0;
110 out[3][0][1] = 0.0;
111 out[3][1][0] = -6.0;
112 out[3][1][1] = -3.0;
113
114 out[4][0][0] = 3.0;
115 out[4][0][1] = 6.0;
116 out[4][1][0] = 0.0;
117 out[4][1][1] = -3.0;
118
119 out[5][0][0] = -3.0;
120 out[5][0][1] = 0.0;
121 out[5][1][0] = 0.0;
122 out[5][1][1] = 3.0;
123 }
124
126 void partial (const std::array<unsigned int, 2>& order,
127 const typename Traits::DomainType& in, // position
128 std::vector<typename Traits::RangeType>& out) const // return value
129 {
130 auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
131 if (totalOrder == 0) {
132 evaluateFunction(in, out);
133 } else if (totalOrder == 1) {
134 out.resize(size());
135 auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
136
137 switch (direction) {
138 case 0:
139 out[0][0] = sign_[0];
140 out[0][1] = 0.0;
141
142 out[1][0] = sign_[1];
143 out[1][1] = 0.0;
144
145 out[2][0] = sign_[2];
146 out[2][1] = 0.0;
147
148 out[3][0] = 3.0;
149 out[3][1] = -6.0;
150
151 out[4][0] = 3.0;
152 out[4][1] = 0.0;
153
154 out[5][0] = -3.0;
155 out[5][1] = 0.0;
156 break;
157 case 1:
158 out[0][0] = 0.0;
159 out[0][1] = sign_[0];
160
161 out[1][0] = 0.0;
162 out[1][1] = sign_[1];
163
164 out[2][0] = 0.0;
165 out[2][1] = sign_[2];
166
167 out[3][0] = 0.0;
168 out[3][1] = -3.0;
169
170 out[4][0] = 6.0;
171 out[4][1] = -3.0;
172
173 out[5][0] = 0.0;
174 out[5][1] = 3.0;
175 break;
176 default:
177 DUNE_THROW(RangeError, "Component out of range.");
178 }
179 } else {
180 DUNE_THROW(NotImplemented, "Desired derivative order is not implemented");
181 }
182 }
183
185 unsigned int order () const
186 {
187 return 1;
188 }
189
190 private:
191 std::array<R,3> sign_;
192 };
193}
194#endif // DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI1_SIMPLEX2D_LOCALBASIS_HH
First order Brezzi-Douglas-Marini shape functions on the reference triangle.
Definition: brezzidouglasmarini1simplex2dlocalbasis.hh:28
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition: brezzidouglasmarini1simplex2dlocalbasis.hh:89
unsigned int size() const
number of shape functions
Definition: brezzidouglasmarini1simplex2dlocalbasis.hh:53
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: brezzidouglasmarini1simplex2dlocalbasis.hh:64
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: brezzidouglasmarini1simplex2dlocalbasis.hh:126
BDM1Simplex2DLocalBasis()
Standard constructor.
Definition: brezzidouglasmarini1simplex2dlocalbasis.hh:35
unsigned int order() const
Polynomial order of the shape functions.
Definition: brezzidouglasmarini1simplex2dlocalbasis.hh:185
BDM1Simplex2DLocalBasis(std::bitset< 3 > s)
Make set number s, where 0 <= s < 8.
Definition: brezzidouglasmarini1simplex2dlocalbasis.hh:46
A dense n x m matrix.
Definition: fmatrix.hh:69
vector space out of a tensor product of fields.
Definition: fvector.hh:95
Default exception for dummy implementations.
Definition: exceptions.hh:261
Default exception class for range errors.
Definition: exceptions.hh:252
Implements a matrix constructed from a given type representing a field and compile-time given number ...
#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
Type traits for LocalBasisVirtualInterface.
Definition: localbasis.hh:32
D DomainType
domain type
Definition: localbasis.hh:43
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