3 #ifndef DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_CUBE2D_LOCALBASIS_HH 4 #define DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_CUBE2D_LOCALBASIS_HH 11 #include <dune/common/fmatrix.hh> 13 #include "../../common/localbasis.hh" 26 template<
class D,
class R>
32 R,2,Dune::FieldVector<R,2>,
38 for (
size_t i=0; i<4; i++)
49 for (
size_t i=0; i<4; i++)
50 sign_[i] = s[i] ? -1.0 : 1.0;
66 std::vector<typename Traits::RangeType>& out)
const 70 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]);
71 out[0][1] = sign_[0]*(-1.25*in[1] + 3.75*in[1]*in[1] - 2.5*in[1]*in[1]*in[1]);
72 out[1][0] = 3.0 - 3.0*in[0]-6.0*in[1] + 6.0*in[0]*in[1];
74 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]);
75 out[2][1] = sign_[0]*(-3.75*in[1] + 11.25*in[1]*in[1] - 7.5*in[1]*in[1]*in[1]);
76 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]);
77 out[3][1] = sign_[1]*(-1.25*in[1] + 3.75*in[1]*in[1] - 2.5*in[1]*in[1]*in[1]);
78 out[4][0] = 3.0*in[0] - 6.0*in[0]*in[1];
80 out[5][0] = sign_[1]*(+3.75*in[0] - 22.5*in[0]*in[1] + 22.5*in[0]*in[1]*in[1]);
81 out[5][1] = sign_[1]*(-3.75*in[1] + 11.25*in[1]*in[1] - 7.5*in[1]*in[1]*in[1]);
82 out[6][0] = sign_[2]*(-1.25*in[0] + 3.75*in[0]*in[0] - 2.5*in[0]*in[0]*in[0]);
83 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]);
85 out[7][1] = -3.0 + 6.0*in[0] + 3.0*in[1] - 6.0*in[0]*in[1];
86 out[8][0] = sign_[2]*(-3.75*in[0] + 11.25*in[0]*in[0] - 7.5*in[0]*in[0]*in[0]);
87 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]);
88 out[9][0] = sign_[3]*(-1.25*in[0] + 3.75*in[0]*in[0] - 2.5*in[0]*in[0]*in[0]);
89 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]);
91 out[10][1] = -3.0*in[1] + 6.0*in[0]*in[1];
92 out[11][0] = sign_[3]*(-3.75*in[0] + 11.25*in[0]*in[0] - 7.5*in[0]*in[0]*in[0]);
93 out[11][1] = sign_[3]*(3.75*in[1] - 22.5*in[0]*in[1] + 22.5*in[0]*in[0]*in[1]);
94 out[12][0] = 6.0*in[0] - 6.0*in[0]*in[0];
97 out[13][1] = 6.0*in[1] - 6.0*in[1]*in[1];
107 std::vector<typename Traits::JacobianType>& out)
const 111 out[0][0][0] = sign_[0]*(5.25 - 7.5*in[1] - 6.0*in[0] + 7.5*in[1]*in[1]);
112 out[0][0][1] = sign_[0]*(7.5 - 7.5*in[0] - 15.0*in[1] + 15.0*in[0]*in[1]);
114 out[0][1][1] = sign_[0]*(-1.25 + 7.5*in[1] - 7.5*in[1]*in[1]);
116 out[1][0][0] = -3.0 + 6.0*in[1];
117 out[1][0][1] = -6.0 + 6.0*in[0];
121 out[2][0][0] = sign_[0]*(3.75 - 22.5*in[1] + 22.5*in[1]*in[1]);
122 out[2][0][1] = sign_[0]*(22.5 - 22.5*in[0] - 45.0*in[1] + 45.0*in[0]*in[1]);
124 out[2][1][1] = sign_[0]*(-3.75 + 22.5*in[1] - 22.5*in[1]*in[1]);
126 out[3][0][0] = sign_[1]*(-0.75 - 7.5*in[1] + 6.0*in[0] + 7.5*in[1]*in[1]);
127 out[3][0][1] = sign_[1]*(-7.5*in[0] + 15.0*in[0]*in[1]);
129 out[3][1][1] = sign_[1]*(-1.25 + 7.5*in[1] - 7.5*in[1]*in[1]);
131 out[4][0][0] = 3.0 - 6.0*in[1];
132 out[4][0][1] = -6.0*in[0];
136 out[5][0][0] = sign_[1]*(3.75 - 22.5*in[1] + 22.5*in[1]*in[1]);
137 out[5][0][1] = sign_[1]*(-22.5*in[0] + 45.0*in[0]*in[1]);
139 out[5][1][1] = sign_[1]*(-3.75 + 22.5*in[1] - 22.5*in[1]*in[1]);
141 out[6][0][0] = sign_[2]*(-1.25 + 7.5*in[0] - 7.5*in[0]*in[0]);
143 out[6][1][0] = sign_[2]*(7.5 - 7.5*in[1] - 15.0*in[0] + 15.0*in[0]*in[1]);
144 out[6][1][1] = sign_[2]*(5.25 - 7.5*in[0]- 6.0*in[1] + 7.5*in[0]*in[0]);
148 out[7][1][0] = 6.0 - 6.0*in[1];
149 out[7][1][1] = 3.0 - 6.0*in[0];
151 out[8][0][0] = sign_[2]*(-3.75 + 22.5*in[0] - 22.5*in[0]*in[0]);
153 out[8][1][0] = sign_[2]*(22.5 - 22.5*in[1] - 45.0*in[0] + 45.0*in[0]*in[1]);
154 out[8][1][1] = sign_[2]*(3.75 - 22.5*in[0] + 22.5*in[0]*in[0]);
156 out[9][0][0] = sign_[3]*(-1.25 + 7.5*in[0] - 7.5*in[0]*in[0]);
158 out[9][1][0] = sign_[3]*(-7.5*in[1] + 15.0*in[0]*in[1]);
159 out[9][1][1] = sign_[3]*(-0.75 - 7.5*in[0] + 6.0*in[1] + 7.5*in[0]*in[0]);
163 out[10][1][0] = 6.0*in[1];
164 out[10][1][1] = -3.0 + 6.0*in[0];
166 out[11][0][0] = sign_[3]*(-3.75 + 22.5*in[0] - 22.5*in[0]*in[0]);
168 out[11][1][0] = sign_[3]*(-22.5*in[1] + 45*in[0]*in[1]);
169 out[11][1][1] = sign_[3]*(3.75 - 22.5*in[0] + 22.5*in[0]*in[0]);
171 out[12][0][0] = 6.0 - 12.0*in[0];
179 out[13][1][1] = 6.0 - 12.0*in[1];
185 std::vector<typename Traits::RangeType>& out)
const 187 auto totalOrder = std::accumulate(
order.begin(),
order.end(), 0);
188 if (totalOrder == 0) {
190 }
else if (totalOrder == 1) {
192 auto const direction = std::distance(
order.begin(), std::find(
order.begin(),
order.end(), 1));
196 out[0][0] = sign_[0]*(5.25 - 7.5*in[1] - 6.0*in[0] + 7.5*in[1]*in[1]);
199 out[1][0] = -3.0 + 6.0*in[1];
202 out[2][0] = sign_[0]*(3.75 - 22.5*in[1] + 22.5*in[1]*in[1]);
205 out[3][0] = sign_[1]*(-0.75 - 7.5*in[1] + 6.0*in[0] + 7.5*in[1]*in[1]);
208 out[4][0] = 3.0 - 6.0*in[1];
211 out[5][0] = sign_[1]*(3.75 - 22.5*in[1] + 22.5*in[1]*in[1]);
214 out[6][0] = sign_[2]*(-1.25 + 7.5*in[0] - 7.5*in[0]*in[0]);
215 out[6][1] = sign_[2]*(7.5 - 7.5*in[1] - 15.0*in[0] + 15.0*in[0]*in[1]);
218 out[7][1] = 6.0 - 6.0*in[1];
220 out[8][0] = sign_[2]*(-3.75 + 22.5*in[0] - 22.5*in[0]*in[0]);
221 out[8][1] = sign_[2]*(22.5 - 22.5*in[1] - 45.0*in[0] + 45.0*in[0]*in[1]);
223 out[9][0] = sign_[3]*(-1.25 + 7.5*in[0] - 7.5*in[0]*in[0]);
224 out[9][1] = sign_[3]*(-7.5*in[1] + 15.0*in[0]*in[1]);
227 out[10][1] = 6.0*in[1];
229 out[11][0] = sign_[3]*(-3.75 + 22.5*in[0] - 22.5*in[0]*in[0]);
230 out[11][1] = sign_[3]*(-22.5*in[1] + 45*in[0]*in[1]);
232 out[12][0] = 6.0 - 12.0*in[0];
239 out[0][0] = sign_[0]*(7.5 - 7.5*in[0] - 15.0*in[1] + 15.0*in[0]*in[1]);
240 out[0][1] = sign_[0]*(-1.25 + 7.5*in[1] - 7.5*in[1]*in[1]);
242 out[1][0] = -6.0 + 6.0*in[0];
245 out[2][0] = sign_[0]*(22.5 - 22.5*in[0] - 45.0*in[1] + 45.0*in[0]*in[1]);
246 out[2][1] = sign_[0]*(-3.75 + 22.5*in[1] - 22.5*in[1]*in[1]);
248 out[3][0] = sign_[1]*(-7.5*in[0] + 15.0*in[0]*in[1]);
249 out[3][1] = sign_[1]*(-1.25 + 7.5*in[1] - 7.5*in[1]*in[1]);
251 out[4][0] = -6.0*in[0];
254 out[5][0] = sign_[1]*(-22.5*in[0] + 45.0*in[0]*in[1]);
255 out[5][1] = sign_[1]*(-3.75 + 22.5*in[1] - 22.5*in[1]*in[1]);
258 out[6][1] = sign_[2]*(5.25 - 7.5*in[0]- 6.0*in[1] + 7.5*in[0]*in[0]);
261 out[7][1] = 3.0 - 6.0*in[0];
264 out[8][1] = sign_[2]*(3.75 - 22.5*in[0] + 22.5*in[0]*in[0]);
267 out[9][1] = sign_[3]*(-0.75 - 7.5*in[0] + 6.0*in[1] + 7.5*in[0]*in[0]);
270 out[10][1] = -3.0 + 6.0*in[0];
273 out[11][1] = sign_[3]*(3.75 - 22.5*in[0] + 22.5*in[0]*in[0]);
279 out[13][1] = 6.0 - 12.0*in[1];
282 DUNE_THROW(RangeError,
"Component out of range.");
285 DUNE_THROW(NotImplemented,
"Desired derivative order is not implemented");
296 std::array<R,4> sign_;
299 #endif // DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_CUBE2D_LOCALBASIS_HH void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:65
unsigned int order() const
Polynomial order of the shape functions.
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:290
Type traits for LocalBasisVirtualInterface.
Definition: localbasis.hh:31
D DomainType
domain type
Definition: localbasis.hh:43
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:183
BDM2Cube2DLocalBasis(std::bitset< 4 > s)
Make set number s, where 0 <= s < 16.
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:47
First order Brezzi-Douglas-Marini shape functions on quadrilaterals.
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:27
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:106
unsigned int size() const
number of shape functions
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:54
Definition: brezzidouglasmarini1cube2dlocalbasis.hh:15
BDM2Cube2DLocalBasis()
Standard constructor.
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:36
LocalBasisTraits< D, 2, Dune::FieldVector< D, 2 >, R, 2, Dune::FieldVector< R, 2 >, Dune::FieldMatrix< R, 2, 2 > > Traits
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:33