Dune Core Modules (2.8.0)

raviartthomas1cube2dlocalbasis.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_RAVIARTTHOMAS1_CUBE2D_LOCALBASIS_HH
4#define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS1_CUBE2D_LOCALBASIS_HH
5
6#include <numeric>
7#include <vector>
8
10
11#include "../../common/localbasis.hh"
12
13namespace Dune
14{
24 template<class D, class R>
26 {
27
28 public:
31
37 RT1Cube2DLocalBasis (std::bitset<4> s = 0)
38 {
39 for (size_t i=0; i<4; i++)
40 sign_[i] = (s[i]) ? -1.0 : 1.0;
41 }
42
44 unsigned int size () const
45 {
46 return 12;
47 }
48
55 inline void evaluateFunction (const typename Traits::DomainType& in,
56 std::vector<typename Traits::RangeType>& out) const
57 {
58 out.resize(12);
59
60 out[0][0] = sign_[0]*(-1.0 + 4.0*in[0]-3*in[0]*in[0]);
61 out[0][1] = 0.0;
62 out[1][0] = 3.0 - 12.0*in[0] - 6.0*in[1] + 24.0*in[0]*in[1]+9*in[0]*in[0] - 18.0*in[0]*in[0]*in[1];
63 out[1][1] = 0.0;
64 out[2][0] = sign_[1]*(-2.0*in[0] + 3.0*in[0]*in[0]);
65 out[2][1] = 0.0;
66 out[3][0] = -6.0*in[0] + 12.0*in[0]*in[1] + 9.0*in[0]*in[0] - 18.0*in[0]*in[0]*in[1];
67 out[3][1] = 0.0;
68 out[4][0] = 0.0;
69 out[4][1] = sign_[2]*(-1.0 + 4.0*in[1] - 3.0*in[1]*in[1]);
70 out[5][0] = 0.0;
71 out[5][1] = -3.0 + 6.0*in[0] + 12.0*in[1] - 24.0*in[0]*in[1] - 9.0*in[1]*in[1] + 18.0*in[0]*in[1]*in[1];
72 out[6][0] = 0.0;
73 out[6][1] = sign_[3]*(-2.0*in[1] + 3.0*in[1]*in[1]);
74 out[7][0] = 0.0;
75 out[7][1] = 6.0*in[1] - 12.0*in[0]*in[1] - 9.0*in[1]*in[1] + 18.0*in[0]*in[1]*in[1];
76 out[8][0] = 24.0*in[0] - 36.0*in[0]*in[1] - 24.0*in[0]*in[0] + 36.0*in[0]*in[0]*in[1];
77 out[8][1] = 0.0;
78 out[9][0] = 0.0;
79 out[9][1] = 24.0*in[1] - 36.0*in[0]*in[1] - 24.0*in[1]*in[1] + 36.0*in[0]*in[1]*in[1];
80 out[10][0] = -36.0*in[0] + 72.0*in[0]*in[1] + 36.0*in[0]*in[0] - 72.0*in[0]*in[0]*in[1];
81 out[10][1] = 0.0;
82 out[11][0] = 0.0;
83 out[11][1] = -36.0*in[1] + 72.0*in[0]*in[1] + 36*in[1]*in[1] - 72.0*in[0]*in[1]*in[1];
84 }
85
92 inline void evaluateJacobian (const typename Traits::DomainType& in,
93 std::vector<typename Traits::JacobianType>& out) const
94 {
95 out.resize(12);
96
97 out[0][0][0] = sign_[0]*(4.0 - 6.0*in[0]);
98 out[0][0][1] = 0.0;
99 out[0][1][0] = 0.0;
100 out[0][1][1] = 0.0;
101
102 out[1][0][0] = -12.0 + 24.0*in[1] + 18.0*in[0] - 36.0*in[0]*in[1];
103 out[1][0][1] = -6 + 24.0*in[0] - 18.0*in[0]*in[0];
104 out[1][1][0] = 0.0;
105 out[1][1][1] = 0.0;
106
107 out[2][0][0] = sign_[1]*(-2.0 + 6.0*in[0]);
108 out[2][0][1] = 0.0;
109 out[2][1][0] = 0.0;
110 out[2][1][1] = 0.0;
111
112 out[3][0][0] = -6.0 + 12.0*in[1] + 18.0*in[0] - 36.0*in[0]*in[1];
113 out[3][0][1] = 12.0*in[0] - 18.0*in[0]*in[0];
114 out[3][1][0] = 0.0;
115 out[3][1][1] = 0.0;
116
117 out[4][0][0] = 0.0;
118 out[4][0][1] = 0.0;
119 out[4][1][0] = 0.0;
120 out[4][1][1] = sign_[2]*(4.0 - 6.0*in[1]);
121
122 out[5][0][0] = 0.0;
123 out[5][0][1] = 0.0;
124 out[5][1][0] = 6.0 - 24.0*in[1] + 18.0*in[1]*in[1];
125 out[5][1][1] = 12.0 - 24.0*in[0] - 18.0*in[1] + 36.0*in[0]*in[1];
126
127 out[6][0][0] = 0.0;
128 out[6][0][1] = 0.0;
129 out[6][1][0] = 0.0;
130 out[6][1][1] = sign_[3]*(-2.0 + 6.0*in[1]);
131
132 out[7][0][0] = 0.0;
133 out[7][0][1] = 0.0;
134 out[7][1][0] = -12.0*in[1] + 18.0*in[1]*in[1];
135 out[7][1][1] = 6.0 - 12.0*in[0] - 18.0*in[1] + 36.0*in[1]*in[0];
136
137 out[8][0][0] = 24.0 - 36.0*in[1] - 48.0*in[0] + 72.0*in[0]*in[1];
138 out[8][0][1] = -36.0*in[0] + 36.0*in[0]*in[0];
139 out[8][1][0] = 0.0;
140 out[8][1][1] = 0.0;
141
142 out[9][0][0] = 0.0;
143 out[9][0][1] = 0.0;
144 out[9][1][0] = -36.0*in[1] + 36.0*in[1]*in[1];
145 out[9][1][1] = 24.0 - 36.0*in[0] - 48.0*in[1] + 72.0*in[0]*in[1];
146
147 out[10][0][0] = -36.0 + 72.0*in[1] + 72.0*in[0] - 144.0*in[0]*in[1];
148 out[10][0][1] = 72.0*in[0] - 72.0*in[0]*in[0];
149 out[10][1][0] = 0.0;
150 out[10][1][1] = 0.0;
151
152 out[11][0][0] = 0.0;
153 out[11][0][1] = 0.0;
154 out[11][1][0] = 72.0*in[1] - 72.0*in[1]*in[1];
155 out[11][1][1] = -36.0 + 72.0*in[0] + 72.0*in[1] - 144.0*in[0]*in[1];
156 }
157
159 void partial (const std::array<unsigned int, 2>& order,
160 const typename Traits::DomainType& in, // position
161 std::vector<typename Traits::RangeType>& out) const // return value
162 {
163 auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
164 if (totalOrder == 0) {
165 evaluateFunction(in, out);
166 } else {
167 DUNE_THROW(NotImplemented, "Desired derivative order is not implemented");
168 }
169 }
170
172 unsigned int order () const
173 {
174 return 3;
175 }
176
177 private:
178 std::array<R,4> sign_;
179 };
180}
181#endif // DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS1_CUBE2D_LOCALBASIS_HH
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
First order Raviart-Thomas shape functions on the reference quadrilateral.
Definition: raviartthomas1cube2dlocalbasis.hh:26
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition: raviartthomas1cube2dlocalbasis.hh:92
unsigned int order() const
Polynomial order of the shape functions.
Definition: raviartthomas1cube2dlocalbasis.hh:172
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: raviartthomas1cube2dlocalbasis.hh:55
unsigned int size() const
number of shape functions
Definition: raviartthomas1cube2dlocalbasis.hh:44
RT1Cube2DLocalBasis(std::bitset< 4 > s=0)
Make set number s, where 0 <= s < 16.
Definition: raviartthomas1cube2dlocalbasis.hh:37
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: raviartthomas1cube2dlocalbasis.hh:159
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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