5#ifndef DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_CUBE2D_LOCALBASIS_HH
6#define DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_CUBE2D_LOCALBASIS_HH
15#include "../../common/localbasis.hh"
28 template<
class D,
class R>
40 for (
size_t i=0; i<4; i++)
51 for (
size_t i=0; i<4; i++)
52 sign_[i] = s[i] ? -1.0 : 1.0;
68 std::vector<typename Traits::RangeType>& out)
const
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];
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];
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]);
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]);
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];
99 out[13][1] = 6.0*in[1] - 6.0*in[1]*in[1];
109 std::vector<typename Traits::JacobianType>& out)
const
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]);
116 out[0][1][1] = sign_[0]*(-1.25 + 7.5*in[1] - 7.5*in[1]*in[1]);
118 out[1][0][0] = -3.0 + 6.0*in[1];
119 out[1][0][1] = -6.0 + 6.0*in[0];
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]);
126 out[2][1][1] = sign_[0]*(-3.75 + 22.5*in[1] - 22.5*in[1]*in[1]);
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]);
131 out[3][1][1] = sign_[1]*(-1.25 + 7.5*in[1] - 7.5*in[1]*in[1]);
133 out[4][0][0] = 3.0 - 6.0*in[1];
134 out[4][0][1] = -6.0*in[0];
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]);
141 out[5][1][1] = sign_[1]*(-3.75 + 22.5*in[1] - 22.5*in[1]*in[1]);
143 out[6][0][0] = sign_[2]*(-1.25 + 7.5*in[0] - 7.5*in[0]*in[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]);
150 out[7][1][0] = 6.0 - 6.0*in[1];
151 out[7][1][1] = 3.0 - 6.0*in[0];
153 out[8][0][0] = sign_[2]*(-3.75 + 22.5*in[0] - 22.5*in[0]*in[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]);
158 out[9][0][0] = sign_[3]*(-1.25 + 7.5*in[0] - 7.5*in[0]*in[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]);
165 out[10][1][0] = 6.0*in[1];
166 out[10][1][1] = -3.0 + 6.0*in[0];
168 out[11][0][0] = sign_[3]*(-3.75 + 22.5*in[0] - 22.5*in[0]*in[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]);
173 out[12][0][0] = 6.0 - 12.0*in[0];
181 out[13][1][1] = 6.0 - 12.0*in[1];
187 std::vector<typename Traits::RangeType>& out)
const
190 if (totalOrder == 0) {
192 }
else if (totalOrder == 1) {
194 auto const direction = std::distance(
order.begin(), std::find(
order.begin(),
order.end(), 1));
198 out[0][0] = sign_[0]*(5.25 - 7.5*in[1] - 6.0*in[0] + 7.5*in[1]*in[1]);
201 out[1][0] = -3.0 + 6.0*in[1];
204 out[2][0] = sign_[0]*(3.75 - 22.5*in[1] + 22.5*in[1]*in[1]);
207 out[3][0] = sign_[1]*(-0.75 - 7.5*in[1] + 6.0*in[0] + 7.5*in[1]*in[1]);
210 out[4][0] = 3.0 - 6.0*in[1];
213 out[5][0] = sign_[1]*(3.75 - 22.5*in[1] + 22.5*in[1]*in[1]);
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]);
220 out[7][1] = 6.0 - 6.0*in[1];
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]);
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]);
229 out[10][1] = 6.0*in[1];
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]);
234 out[12][0] = 6.0 - 12.0*in[0];
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]);
244 out[1][0] = -6.0 + 6.0*in[0];
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]);
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]);
253 out[4][0] = -6.0*in[0];
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]);
260 out[6][1] = sign_[2]*(5.25 - 7.5*in[0]- 6.0*in[1] + 7.5*in[0]*in[0]);
263 out[7][1] = 3.0 - 6.0*in[0];
266 out[8][1] = sign_[2]*(3.75 - 22.5*in[0] + 22.5*in[0]*in[0]);
269 out[9][1] = sign_[3]*(-0.75 - 7.5*in[0] + 6.0*in[1] + 7.5*in[0]*in[0]);
272 out[10][1] = -3.0 + 6.0*in[0];
275 out[11][1] = sign_[3]*(3.75 - 22.5*in[0] + 22.5*in[0]*in[0]);
281 out[13][1] = 6.0 - 12.0*in[1];
298 std::array<R,4> sign_;
First order Brezzi-Douglas-Marini shape functions on quadrilaterals.
Definition: brezzidouglasmarini2cube2dlocalbasis.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: brezzidouglasmarini2cube2dlocalbasis.hh:185
unsigned int order() const
Polynomial order of the shape functions.
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:292
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:67
BDM2Cube2DLocalBasis()
Standard constructor.
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:38
BDM2Cube2DLocalBasis(std::bitset< 4 > s)
Make set number s, where 0 <= s < 16.
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:49
unsigned int size() const
number of shape functions
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:56
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:108
A dense n x m matrix.
Definition: fmatrix.hh:117
vector space out of a tensor product of fields.
Definition: fvector.hh:91
Default exception for dummy implementations.
Definition: exceptions.hh:263
Default exception class for range errors.
Definition: exceptions.hh:254
Implements a matrix constructed from a given type representing a field and compile-time given number ...
#define DUNE_THROW(E, m)
Definition: exceptions.hh:218
constexpr T accumulate(Range &&range, T value, F &&f)
Accumulate values.
Definition: hybridutilities.hh:279
Dune namespace.
Definition: alignedallocator.hh:13
Type traits for LocalBasisVirtualInterface.
Definition: localbasis.hh:35
D DomainType
domain type
Definition: localbasis.hh:43