3 #ifndef DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS0_CUBE2D_ALL_HH 4 #define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS0_CUBE2D_ALL_HH 10 #include <dune/common/fmatrix.hh> 25 template<
class D,
class R>
35 sign0 = sign1 = sign2 = sign3 = 1.0;
41 sign0 = sign1 = sign2 = sign3 = 1.0;
42 if (s&1) sign0 = -1.0;
43 if (s&2) sign1 = -1.0;
44 if (s&4) sign2 = -1.0;
45 if (s&8) sign3 = -1.0;
56 std::vector<typename Traits::RangeType>& out)
const 59 out[0][0] = sign0*(in[0]-1.0); out[0][1]=0.0;
60 out[1][0] = sign1*(in[0]); out[1][1]=0.0;
61 out[2][0] = 0.0; out[2][1]=sign2*(in[1]-1.0);
62 out[3][0] = 0.0; out[3][1]=sign3*(in[1]);
68 std::vector<typename Traits::JacobianType>& out)
const 71 out[0][0][0] = sign0; out[0][0][1] = 0;
72 out[0][1][0] = 0; out[0][1][1] = 0;
74 out[1][0][0] = sign1; out[1][0][1] = 0;
75 out[1][1][0] = 0; out[1][1][1] = 0;
77 out[2][0][0] = 0; out[2][0][1] = 0;
78 out[2][1][0] = 0; out[2][1][1] = sign2;
80 out[3][0][0] = 0; out[3][0][1] = 0;
81 out[3][1][0] = 0; out[3][1][1] = sign3;
87 std::vector<typename Traits::RangeType>& out)
const 89 auto totalOrder = std::accumulate(
order.begin(),
order.end(), 0);
90 if (totalOrder == 0) {
92 }
else if (totalOrder == 1) {
93 auto const direction = std::distance(
order.begin(), std::find(
order.begin(),
order.end(), 1));
96 for (std::size_t i = 0; i <
size(); ++i)
97 out[i][0] = out[i][1] = 0;
109 DUNE_THROW(RangeError,
"Component out of range.");
113 for (std::size_t i = 0; i <
size(); ++i)
114 for (std::size_t j = 0; j < 2; ++j)
127 R sign0, sign1, sign2, sign3;
146 sign0 = sign1 = sign2 = sign3 = 1.0;
152 sign0 = sign1 = sign2 = sign3 = 1.0;
153 if (s&1) sign0 *= -1.0;
154 if (s&2) sign1 *= -1.0;
155 if (s&4) sign2 *= -1.0;
156 if (s&8) sign3 *= -1.0;
158 m0[0] = 0.0; m0[1] = 0.5;
159 m1[0] = 1.0; m1[1] = 0.5;
160 m2[0] = 0.5; m2[1] = 0.0;
161 m3[0] = 0.5; m3[1] = 1.0;
163 n0[0] = -1.0; n0[1] = 0.0;
164 n1[0] = 1.0; n1[1] = 0.0;
165 n2[0] = 0.0; n2[1] = -1.0;
166 n3[0] = 0.0; n3[1] = 1.0;
169 template<
typename F,
typename C>
173 typename F::Traits::RangeType y;
177 f.evaluate(m0,y); out[0] = (y[0]*n0[0]+y[1]*n0[1])*sign0;
178 f.evaluate(m1,y); out[1] = (y[0]*n1[0]+y[1]*n1[1])*sign1;
179 f.evaluate(m2,y); out[2] = (y[0]*n2[0]+y[1]*n2[1])*sign2;
180 f.evaluate(m3,y); out[3] = (y[0]*n3[0]+y[1]*n3[1])*sign3;
184 typename LB::Traits::RangeFieldType sign0,sign1,sign2,sign3;
185 typename LB::Traits::DomainType m0,m1,m2,m3;
186 typename LB::Traits::DomainType n0,n1,n2,n3;
201 for (std::size_t i=0; i<4; i++)
218 std::vector<LocalKey> li;
222 #endif // DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS0_CUBE2D_ALL_HH RT0Cube2DLocalInterpolation()
Standard constructor.
Definition: raviartthomas0cube2dall.hh:144
Lowest order Raviart-Thomas shape functions on the reference quadrilateral.
Definition: raviartthomas0cube2dall.hh:26
LocalBasisTraits< D, 2, Dune::FieldVector< D, 2 >, R, 2, Dune::FieldVector< R, 2 >, Dune::FieldMatrix< R, 2, 2 > > Traits
Definition: raviartthomas0cube2dall.hh:30
RT0Cube2DLocalInterpolation(unsigned int s)
Make set numer s, where 0<=s<8.
Definition: raviartthomas0cube2dall.hh:150
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: raviartthomas0cube2dall.hh:85
RT0Cube2DLocalCoefficients()
Standard constructor.
Definition: raviartthomas0cube2dall.hh:199
Definition: brezzidouglasmarini1cube2dlocalbasis.hh:15
unsigned int order() const
Polynomial order of the shape functions.
Definition: raviartthomas0cube2dall.hh:121
void interpolate(const F &f, std::vector< C > &out) const
Definition: raviartthomas0cube2dall.hh:170
unsigned int size() const
number of shape functions
Definition: raviartthomas0cube2dall.hh:49
D DomainType
domain type
Definition: localbasis.hh:49
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition: raviartthomas0cube2dall.hh:67
RT0Cube2DLocalBasis()
Standard constructor.
Definition: raviartthomas0cube2dall.hh:33
std::size_t size() const
number of coefficients
Definition: raviartthomas0cube2dall.hh:206
Layout map for RT0 elements on quadrilaterals.
Definition: raviartthomas0cube2dall.hh:195
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: raviartthomas0cube2dall.hh:55
const LocalKey & localKey(std::size_t i) const
get i'th index
Definition: raviartthomas0cube2dall.hh:212
Type traits for LocalBasisVirtualInterface.
Definition: localbasis.hh:37
Lowest order Raviart-Thomas shape functions on the reference quadrilateral.
Definition: raviartthomas0cube2dall.hh:139
Describe position of one degree of freedom.
Definition: localkey.hh:20
RT0Cube2DLocalBasis(unsigned int s)
Make set numer s, where 0<=s<16.
Definition: raviartthomas0cube2dall.hh:39