5#ifndef DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS1_CUBE2D_LOCALINTERPOLATION_HH
6#define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS1_CUBE2D_LOCALINTERPOLATION_HH
36 for (
size_t i=0; i<4; i++)
37 sign_[i] = (s[i]) ? -1.0 : 1.0;
53 template<
class F,
class C>
57 typedef typename LB::Traits::RangeFieldType
Scalar;
58 typedef typename LB::Traits::DomainFieldType Vector;
61 fill(out.begin(), out.end(), 0.0);
66 for (
auto&& qp : rule1)
68 Scalar qPos = qp.position();
69 typename LB::Traits::DomainType localPos = {0.0, qPos};
72 out[0] += (y[0]*n_[0][0] + y[1]*n_[0][1])*qp.weight()*sign_[0];
73 out[1] += (y[0]*n_[0][0] + y[1]*n_[0][1])*(2.0*qPos - 1.0)*qp.weight();
75 localPos = {1.0, qPos};
77 out[2] += (y[0]*n_[1][0] + y[1]*n_[1][1])*qp.weight()*sign_[1];
78 out[3] += (y[0]*n_[1][0] + y[1]*n_[1][1])*(1.0 - 2.0*qPos)*qp.weight();
80 localPos = {qPos, 0.0};
82 out[4] += (y[0]*n_[2][0] + y[1]*n_[2][1])*qp.weight()*sign_[2];
83 out[5] += (y[0]*n_[2][0] + y[1]*n_[2][1])*(1.0 - 2.0*qPos)*qp.weight();
85 localPos = {qPos, 1.0};
87 out[6] += (y[0]*n_[3][0] + y[1]*n_[3][1])*qp.weight()*sign_[3];
88 out[7] += (y[0]*n_[3][0] + y[1]*n_[3][1])*(2.0*qPos - 1.0)*qp.weight();
93 for (
auto&& qp : rule2)
95 auto qPos = qp.position();
98 out[8] += y[0]*qp.weight();
99 out[9] += y[1]*qp.weight();
100 out[10] += y[0]*qPos[1]*qp.weight();
101 out[11] += y[1]*qPos[0]*qp.weight();
107 std::array<typename LB::Traits::RangeFieldType, 4> sign_;
110 std::array<typename LB::Traits::DomainType, 4> n_;
static const QuadratureRule & rule(const GeometryType &t, int p, QuadratureType::Enum qt=QuadratureType::GaussLegendre)
select the appropriate QuadratureRule for GeometryType t and order p
Definition: quadraturerules.hh:326
First order Raviart-Thomas shape functions on the reference quadrilateral.
Definition: raviartthomas1cube2dlocalinterpolation.hh:26
void interpolate(const F &f, std::vector< C > &out) const
Interpolate a given function with shape functions.
Definition: raviartthomas1cube2dlocalinterpolation.hh:54
RT1Cube2DLocalInterpolation(std::bitset< 4 > s=0)
Make set number s, where 0 <= s < 16.
Definition: raviartthomas1cube2dlocalinterpolation.hh:34
constexpr GeometryType cube(unsigned int dim)
Returns a GeometryType representing a hypercube of dimension dim.
Definition: type.hh:462
typename Overloads::ScalarType< std::decay_t< V > >::type Scalar
Element type of some SIMD type.
Definition: interface.hh:235
Dune namespace.
Definition: alignedallocator.hh:13