3#ifndef DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS2_CUBE2D_LOCALINTERPOLATION_HH
4#define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS2_CUBE2D_LOCALINTERPOLATION_HH
8#include <dune/geometry/quadraturerules.hh>
35 for (
size_t i=0; i<4; i++)
36 sign_[i] = (s[i]) ? -1.0 : 1.0;
52 template<
typename F,
typename C>
56 typedef typename LB::Traits::RangeFieldType Scalar;
57 typedef typename LB::Traits::DomainFieldType Vector;
59 auto&& f = Impl::makeFunctionWithCallOperator<typename LB::Traits::DomainType>(ff);
62 fill(out.begin(), out.end(), 0.0);
65 const auto& rule1 = QuadratureRules<Scalar,1>::rule(GeometryTypes::cube(1), qOrder);
67 for (
auto&& qp : rule1)
69 Scalar qPos = qp.position();
70 typename LB::Traits::DomainType localPos;
72 localPos = {0.0, qPos};
74 out[0] += (y[0]*n_[0][0] + y[1]*n_[0][1])*qp.weight()*sign_[0];
75 out[1] += (y[0]*n_[0][0] + y[1]*n_[0][1])*(2.0*qPos - 1.0)*qp.weight();
76 out[2] += (y[0]*n_[0][0] + y[1]*n_[0][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[0];
78 localPos = {1.0, qPos};
80 out[3] += (y[0]*n_[1][0] + y[1]*n_[1][1])*qp.weight()*sign_[1];
81 out[4] += (y[0]*n_[1][0] + y[1]*n_[1][1])*(1.0 - 2.0*qPos)*qp.weight();
82 out[5] += (y[0]*n_[1][0] + y[1]*n_[1][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[1];
84 localPos = {qPos, 0.0};
86 out[6] += (y[0]*n_[2][0] + y[1]*n_[2][1])*qp.weight()*sign_[2];
87 out[7] += (y[0]*n_[2][0] + y[1]*n_[2][1])*(1.0 - 2.0*qPos)*qp.weight();
88 out[8] += (y[0]*n_[2][0] + y[1]*n_[2][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[2];
90 localPos = {qPos, 1.0};
92 out[9] += (y[0]*n_[3][0] + y[1]*n_[3][1])*qp.weight()*sign_[3];
93 out[10] += (y[0]*n_[3][0] + y[1]*n_[3][1])*(2.0*qPos - 1.0)*qp.weight();
94 out[11] += (y[0]*n_[3][0] + y[1]*n_[3][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[3];
97 const auto& rule2 = QuadratureRules<Vector,2>::rule(GeometryTypes::cube(2), qOrder);
99 for (
auto&& qp : rule2)
101 FieldVector<double,2> qPos = qp.position();
104 out[12] += y[0]*qp.weight();
105 out[13] += y[1]*qp.weight();
106 out[14] += y[0]*qPos[0]*qp.weight();
107 out[15] += y[1]*qPos[0]*qp.weight();
108 out[16] += y[0]*qPos[1]*qp.weight();
109 out[17] += y[1]*qPos[1]*qp.weight();
110 out[18] += y[0]*qPos[0]*qPos[1]*qp.weight();
111 out[19] += y[1]*qPos[0]*qPos[1]*qp.weight();
112 out[20] += y[0]*qPos[1]*qPos[1]*qp.weight();
113 out[21] += y[1]*qPos[0]*qPos[0]*qp.weight();
114 out[22] += y[0]*qPos[0]*qPos[1]*qPos[1]*qp.weight();
115 out[23] += y[1]*qPos[0]*qPos[0]*qPos[1]*qp.weight();
121 std::array<typename LB::Traits::RangeFieldType, 4> sign_;
124 std::array<typename LB::Traits::DomainType, 4> n_;
Definition: bdfmcube.hh:16
Second order Raviart-Thomas shape functions on the reference triangle.
Definition: raviartthomas2cube2dlocalinterpolation.hh:24
void interpolate(const F &ff, std::vector< C > &out) const
Interpolate a given function with shape functions.
Definition: raviartthomas2cube2dlocalinterpolation.hh:53
RT2Cube2DLocalInterpolation(std::bitset< 4 > s=0)
Make set number s, where 0 <= s < 16.
Definition: raviartthomas2cube2dlocalinterpolation.hh:33