Dune Core Modules (unstable)

brezzidouglasmarini2cube2dlocalbasis.hh
1// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
2// vi: set et ts=4 sw=2 sts=2:
3// SPDX-FileCopyrightInfo: Copyright © DUNE Project contributors, see file LICENSE.md in module root
4// SPDX-License-Identifier: LicenseRef-GPL-2.0-only-with-DUNE-exception
5#ifndef DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_CUBE2D_LOCALBASIS_HH
6#define DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_CUBE2D_LOCALBASIS_HH
7
8#include <array>
9#include <bitset>
10#include <numeric>
11#include <vector>
12
13#include <dune/common/fmatrix.hh>
14
15#include "../../common/localbasis.hh"
16
17namespace Dune
18{
28 template<class D, class R>
29 class BDM2Cube2DLocalBasis
30 {
31
32 public:
33 typedef LocalBasisTraits<D,2,Dune::FieldVector<D,2>,
34 R,2,Dune::FieldVector<R,2>,
35 Dune::FieldMatrix<R,2,2> > Traits;
36
38 BDM2Cube2DLocalBasis()
39 {
40 for (size_t i=0; i<4; i++)
41 sign_[i] = 1.0;
42 }
43
49 BDM2Cube2DLocalBasis(std::bitset<4> s)
50 {
51 for (size_t i=0; i<4; i++)
52 sign_[i] = s[i] ? -1.0 : 1.0;
53 }
54
56 unsigned int size() const
57 {
58 return 14;
59 }
60
67 inline void evaluateFunction(const typename Traits::DomainType& in,
68 std::vector<typename Traits::RangeType>& out) const
69 {
70 out.resize(size());
71
72 out[0][0] = sign_[0]*(-2.25 + 5.25*in[0] + 7.5*in[1] - 7.5*in[0]*in[1] - 3.0*in[0]*in[0] - 7.5*in[1]*in[1] + 7.5*in[0]*in[1]*in[1]);
73 out[0][1] = sign_[0]*(-1.25*in[1] + 3.75*in[1]*in[1] - 2.5*in[1]*in[1]*in[1]);
74 out[1][0] = 3.0 - 3.0*in[0]-6.0*in[1] + 6.0*in[0]*in[1];
75 out[1][1] = 0.0;
76 out[2][0] = sign_[0]*(-3.75 + 3.75*in[0] + 22.5*in[1] - 22.5*in[0]*in[1] - 22.5*in[1]*in[1] + 22.5*in[0]*in[1]*in[1]);
77 out[2][1] = sign_[0]*(-3.75*in[1] + 11.25*in[1]*in[1] - 7.5*in[1]*in[1]*in[1]);
78 out[3][0] = sign_[1]*(-0.75*in[0] - 7.5*in[0]*in[1] + 3.0*in[0]*in[0] + 7.5*in[0]*in[1]*in[1]);
79 out[3][1] = sign_[1]*(-1.25*in[1] + 3.75*in[1]*in[1] - 2.5*in[1]*in[1]*in[1]);
80 out[4][0] = 3.0*in[0] - 6.0*in[0]*in[1];
81 out[4][1] = 0.0;
82 out[5][0] = sign_[1]*(+3.75*in[0] - 22.5*in[0]*in[1] + 22.5*in[0]*in[1]*in[1]);
83 out[5][1] = sign_[1]*(-3.75*in[1] + 11.25*in[1]*in[1] - 7.5*in[1]*in[1]*in[1]);
84 out[6][0] = sign_[2]*(-1.25*in[0] + 3.75*in[0]*in[0] - 2.5*in[0]*in[0]*in[0]);
85 out[6][1] = sign_[2]*(-2.25 + 7.5*in[0] + 5.25*in[1] - 7.5*in[0]*in[1] - 7.5*in[0]*in[0] - 3.0*in[1]*in[1] + 7.5*in[0]*in[0]*in[1]);
86 out[7][0] = 0.0;
87 out[7][1] = -3.0 + 6.0*in[0] + 3.0*in[1] - 6.0*in[0]*in[1];
88 out[8][0] = sign_[2]*(-3.75*in[0] + 11.25*in[0]*in[0] - 7.5*in[0]*in[0]*in[0]);
89 out[8][1] = sign_[2]*(-3.75 + 22.5*in[0] + 3.75*in[1] - 22.5*in[0]*in[1] - 22.5*in[0]*in[0] + 22.5*in[0]*in[0]*in[1]);
90 out[9][0] = sign_[3]*(-1.25*in[0] + 3.75*in[0]*in[0] - 2.5*in[0]*in[0]*in[0]);
91 out[9][1] = sign_[3]*(-0.75*in[1] - 7.5*in[0]*in[1] + 3.0*in[1]*in[1] + 7.5*in[0]*in[0]*in[1]);
92 out[10][0] = 0.0;
93 out[10][1] = -3.0*in[1] + 6.0*in[0]*in[1];
94 out[11][0] = sign_[3]*(-3.75*in[0] + 11.25*in[0]*in[0] - 7.5*in[0]*in[0]*in[0]);
95 out[11][1] = sign_[3]*(3.75*in[1] - 22.5*in[0]*in[1] + 22.5*in[0]*in[0]*in[1]);
96 out[12][0] = 6.0*in[0] - 6.0*in[0]*in[0];
97 out[12][1] = 0.0;
98 out[13][0] = 0.0;
99 out[13][1] = 6.0*in[1] - 6.0*in[1]*in[1];
100 }
101
108 inline void evaluateJacobian(const typename Traits::DomainType& in,
109 std::vector<typename Traits::JacobianType>& out) const
110 {
111 out.resize(size());
112
113 out[0][0][0] = sign_[0]*(5.25 - 7.5*in[1] - 6.0*in[0] + 7.5*in[1]*in[1]);
114 out[0][0][1] = sign_[0]*(7.5 - 7.5*in[0] - 15.0*in[1] + 15.0*in[0]*in[1]);
115 out[0][1][0] = 0.0;
116 out[0][1][1] = sign_[0]*(-1.25 + 7.5*in[1] - 7.5*in[1]*in[1]);
117
118 out[1][0][0] = -3.0 + 6.0*in[1];
119 out[1][0][1] = -6.0 + 6.0*in[0];
120 out[1][1][0] = 0.0;
121 out[1][1][1] = 0.0;
122
123 out[2][0][0] = sign_[0]*(3.75 - 22.5*in[1] + 22.5*in[1]*in[1]);
124 out[2][0][1] = sign_[0]*(22.5 - 22.5*in[0] - 45.0*in[1] + 45.0*in[0]*in[1]);
125 out[2][1][0] = 0.0;
126 out[2][1][1] = sign_[0]*(-3.75 + 22.5*in[1] - 22.5*in[1]*in[1]);
127
128 out[3][0][0] = sign_[1]*(-0.75 - 7.5*in[1] + 6.0*in[0] + 7.5*in[1]*in[1]);
129 out[3][0][1] = sign_[1]*(-7.5*in[0] + 15.0*in[0]*in[1]);
130 out[3][1][0] = 0.0;
131 out[3][1][1] = sign_[1]*(-1.25 + 7.5*in[1] - 7.5*in[1]*in[1]);
132
133 out[4][0][0] = 3.0 - 6.0*in[1];
134 out[4][0][1] = -6.0*in[0];
135 out[4][1][0] = 0.0;
136 out[4][1][1] = 0.0;
137
138 out[5][0][0] = sign_[1]*(3.75 - 22.5*in[1] + 22.5*in[1]*in[1]);
139 out[5][0][1] = sign_[1]*(-22.5*in[0] + 45.0*in[0]*in[1]);
140 out[5][1][0] = 0.0;
141 out[5][1][1] = sign_[1]*(-3.75 + 22.5*in[1] - 22.5*in[1]*in[1]);
142
143 out[6][0][0] = sign_[2]*(-1.25 + 7.5*in[0] - 7.5*in[0]*in[0]);
144 out[6][0][1] = 0.0;
145 out[6][1][0] = sign_[2]*(7.5 - 7.5*in[1] - 15.0*in[0] + 15.0*in[0]*in[1]);
146 out[6][1][1] = sign_[2]*(5.25 - 7.5*in[0]- 6.0*in[1] + 7.5*in[0]*in[0]);
147
148 out[7][0][0] = 0.0;
149 out[7][0][1] = 0.0;
150 out[7][1][0] = 6.0 - 6.0*in[1];
151 out[7][1][1] = 3.0 - 6.0*in[0];
152
153 out[8][0][0] = sign_[2]*(-3.75 + 22.5*in[0] - 22.5*in[0]*in[0]);
154 out[8][0][1] = 0.0;
155 out[8][1][0] = sign_[2]*(22.5 - 22.5*in[1] - 45.0*in[0] + 45.0*in[0]*in[1]);
156 out[8][1][1] = sign_[2]*(3.75 - 22.5*in[0] + 22.5*in[0]*in[0]);
157
158 out[9][0][0] = sign_[3]*(-1.25 + 7.5*in[0] - 7.5*in[0]*in[0]);
159 out[9][0][1] = 0.0;
160 out[9][1][0] = sign_[3]*(-7.5*in[1] + 15.0*in[0]*in[1]);
161 out[9][1][1] = sign_[3]*(-0.75 - 7.5*in[0] + 6.0*in[1] + 7.5*in[0]*in[0]);
162
163 out[10][0][0] = 0.0;
164 out[10][0][1] = 0.0;
165 out[10][1][0] = 6.0*in[1];
166 out[10][1][1] = -3.0 + 6.0*in[0];
167
168 out[11][0][0] = sign_[3]*(-3.75 + 22.5*in[0] - 22.5*in[0]*in[0]);
169 out[11][0][1] = 0.0;
170 out[11][1][0] = sign_[3]*(-22.5*in[1] + 45*in[0]*in[1]);
171 out[11][1][1] = sign_[3]*(3.75 - 22.5*in[0] + 22.5*in[0]*in[0]);
172
173 out[12][0][0] = 6.0 - 12.0*in[0];
174 out[12][0][1] = 0.0;
175 out[12][1][0] = 0.0;
176 out[12][1][1] = 0.0;
177
178 out[13][0][0] = 0.0;
179 out[13][0][1] = 0.0;
180 out[13][1][0] = 0.0;
181 out[13][1][1] = 6.0 - 12.0*in[1];
182 }
183
185 void partial (const std::array<unsigned int, 2>& order,
186 const typename Traits::DomainType& in, // position
187 std::vector<typename Traits::RangeType>& out) const // return value
188 {
189 auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
190 if (totalOrder == 0) {
191 evaluateFunction(in, out);
192 } else if (totalOrder == 1) {
193 out.resize(size());
194 auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
195
196 switch (direction) {
197 case 0:
198 out[0][0] = sign_[0]*(5.25 - 7.5*in[1] - 6.0*in[0] + 7.5*in[1]*in[1]);
199 out[0][1] = 0.0;
200
201 out[1][0] = -3.0 + 6.0*in[1];
202 out[1][1] = 0.0;
203
204 out[2][0] = sign_[0]*(3.75 - 22.5*in[1] + 22.5*in[1]*in[1]);
205 out[2][1] = 0.0;
206
207 out[3][0] = sign_[1]*(-0.75 - 7.5*in[1] + 6.0*in[0] + 7.5*in[1]*in[1]);
208 out[3][1] = 0.0;
209
210 out[4][0] = 3.0 - 6.0*in[1];
211 out[4][1] = 0.0;
212
213 out[5][0] = sign_[1]*(3.75 - 22.5*in[1] + 22.5*in[1]*in[1]);
214 out[5][1] = 0.0;
215
216 out[6][0] = sign_[2]*(-1.25 + 7.5*in[0] - 7.5*in[0]*in[0]);
217 out[6][1] = sign_[2]*(7.5 - 7.5*in[1] - 15.0*in[0] + 15.0*in[0]*in[1]);
218
219 out[7][0] = 0.0;
220 out[7][1] = 6.0 - 6.0*in[1];
221
222 out[8][0] = sign_[2]*(-3.75 + 22.5*in[0] - 22.5*in[0]*in[0]);
223 out[8][1] = sign_[2]*(22.5 - 22.5*in[1] - 45.0*in[0] + 45.0*in[0]*in[1]);
224
225 out[9][0] = sign_[3]*(-1.25 + 7.5*in[0] - 7.5*in[0]*in[0]);
226 out[9][1] = sign_[3]*(-7.5*in[1] + 15.0*in[0]*in[1]);
227
228 out[10][0] = 0.0;
229 out[10][1] = 6.0*in[1];
230
231 out[11][0] = sign_[3]*(-3.75 + 22.5*in[0] - 22.5*in[0]*in[0]);
232 out[11][1] = sign_[3]*(-22.5*in[1] + 45*in[0]*in[1]);
233
234 out[12][0] = 6.0 - 12.0*in[0];
235 out[12][1] = 0.0;
236
237 out[13][0] = 0.0;
238 out[13][1] = 0.0;
239 break;
240 case 1:
241 out[0][0] = sign_[0]*(7.5 - 7.5*in[0] - 15.0*in[1] + 15.0*in[0]*in[1]);
242 out[0][1] = sign_[0]*(-1.25 + 7.5*in[1] - 7.5*in[1]*in[1]);
243
244 out[1][0] = -6.0 + 6.0*in[0];
245 out[1][1] = 0.0;
246
247 out[2][0] = sign_[0]*(22.5 - 22.5*in[0] - 45.0*in[1] + 45.0*in[0]*in[1]);
248 out[2][1] = sign_[0]*(-3.75 + 22.5*in[1] - 22.5*in[1]*in[1]);
249
250 out[3][0] = sign_[1]*(-7.5*in[0] + 15.0*in[0]*in[1]);
251 out[3][1] = sign_[1]*(-1.25 + 7.5*in[1] - 7.5*in[1]*in[1]);
252
253 out[4][0] = -6.0*in[0];
254 out[4][1] = 0.0;
255
256 out[5][0] = sign_[1]*(-22.5*in[0] + 45.0*in[0]*in[1]);
257 out[5][1] = sign_[1]*(-3.75 + 22.5*in[1] - 22.5*in[1]*in[1]);
258
259 out[6][0] = 0.0;
260 out[6][1] = sign_[2]*(5.25 - 7.5*in[0]- 6.0*in[1] + 7.5*in[0]*in[0]);
261
262 out[7][0] = 0.0;
263 out[7][1] = 3.0 - 6.0*in[0];
264
265 out[8][0] = 0.0;
266 out[8][1] = sign_[2]*(3.75 - 22.5*in[0] + 22.5*in[0]*in[0]);
267
268 out[9][0] = 0.0;
269 out[9][1] = sign_[3]*(-0.75 - 7.5*in[0] + 6.0*in[1] + 7.5*in[0]*in[0]);
270
271 out[10][0] = 0.0;
272 out[10][1] = -3.0 + 6.0*in[0];
273
274 out[11][0] = 0.0;
275 out[11][1] = sign_[3]*(3.75 - 22.5*in[0] + 22.5*in[0]*in[0]);
276
277 out[12][0] = 0.0;
278 out[12][1] = 0.0;
279
280 out[13][0] = 0.0;
281 out[13][1] = 6.0 - 12.0*in[1];
282 break;
283 default:
284 DUNE_THROW(RangeError, "Component out of range.");
285 }
286 } else {
287 DUNE_THROW(NotImplemented, "Desired derivative order is not implemented");
288 }
289 }
290
292 unsigned int order() const
293 {
294 return 3;
295 }
296
297 private:
298 std::array<R,4> sign_;
299 };
300} // end namespace Dune
301#endif // DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_CUBE2D_LOCALBASIS_HH
Dune::BDM2Cube2DLocalBasis
First order Brezzi-Douglas-Marini shape functions on quadrilaterals.
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:30
Dune::BDM2Cube2DLocalBasis::partial
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: brezzidouglasmarini2cube2dlocalbasis.hh:185
Dune::BDM2Cube2DLocalBasis::order
unsigned int order() const
Polynomial order of the shape functions.
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:292
Dune::BDM2Cube2DLocalBasis::evaluateFunction
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:67
Dune::BDM2Cube2DLocalBasis::BDM2Cube2DLocalBasis
BDM2Cube2DLocalBasis()
Standard constructor.
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:38
Dune::BDM2Cube2DLocalBasis::BDM2Cube2DLocalBasis
BDM2Cube2DLocalBasis(std::bitset< 4 > s)
Make set number s, where 0 <= s < 16.
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:49
Dune::BDM2Cube2DLocalBasis::size
unsigned int size() const
number of shape functions
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:56
Dune::BDM2Cube2DLocalBasis::evaluateJacobian
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:108
Dune::FieldMatrix
A dense n x m matrix.
Definition: fmatrix.hh:117
Dune::FieldVector
vector space out of a tensor product of fields.
Definition: fvector.hh:91
Dune::NotImplemented
Default exception for dummy implementations.
Definition: exceptions.hh:263
Dune::RangeError
Default exception class for range errors.
Definition: exceptions.hh:254
fmatrix.hh
Implements a matrix constructed from a given type representing a field and compile-time given number ...
DUNE_THROW
#define DUNE_THROW(E, m)
Definition: exceptions.hh:218
Dune::Hybrid::accumulate
constexpr T accumulate(Range &&range, T value, F &&f)
Accumulate values.
Definition: hybridutilities.hh:279
Dune
Dune namespace.
Definition: alignedallocator.hh:13
Dune::LocalBasisTraits
Type traits for LocalBasisVirtualInterface.
Definition: localbasis.hh:35
Dune::LocalBasisTraits::DomainType
D DomainType
domain type
Definition: localbasis.hh:43
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