3#ifndef DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS4_CUBE2D_LOCALINTERPOLATION_HH
4#define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS4_CUBE2D_LOCALINTERPOLATION_HH
8#include <dune/geometry/quadraturerules.hh>
35 sign0 = sign1 = sign2 = sign3 = 1.0;
71 template<
typename F,
typename C>
75 typedef typename LB::Traits::RangeFieldType Scalar;
76 typedef typename LB::Traits::DomainFieldType Vector;
78 auto&& f = Impl::makeFunctionWithCallOperator<typename LB::Traits::DomainType>(ff);
81 fill(out.begin(), out.end(), 0.0);
83 const int qOrder = 12;
84 const QuadratureRule<Scalar,1>& rule = QuadratureRules<Scalar,1>::rule(GeometryTypes::cube(1), qOrder);
86 for (
typename QuadratureRule<Scalar,1>::const_iterator it=rule.begin(); it!=rule.end(); ++it)
88 Scalar qPos = it->position();
89 typename LB::Traits::DomainType localPos;
94 out[0] += (y[0]*n0[0] + y[1]*n0[1])*it->weight()*sign0;
95 out[1] += (y[0]*n0[0] + y[1]*n0[1])*(2.0*qPos - 1.0)*it->weight();
96 out[2] += (y[0]*n0[0] + y[1]*n0[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign0;
97 out[3] += (y[0]*n0[0] + y[1]*n0[1])*(20.0*qPos*qPos*qPos - 30.0*qPos*qPos + 12.0*qPos - 1.0)*it->weight();
98 out[4] += (y[0]*n0[0] + y[1]*n0[1])*(1.0-20.0*qPos+90.0*pow(qPos,2)-140.0*pow(qPos,3)+70.0*pow(qPos,4))*it->weight()*sign0;
103 out[5] += (y[0]*n1[0] + y[1]*n1[1])*it->weight()*sign1;
104 out[6] += (y[0]*n1[0] + y[1]*n1[1])*(1.0 - 2.0*qPos)*it->weight();
105 out[7] += (y[0]*n1[0] + y[1]*n1[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign1;
106 out[8] += (y[0]*n1[0] + y[1]*n1[1])*(-20.0*qPos*qPos*qPos + 30.0*qPos*qPos - 12.0*qPos + 1.0)*it->weight();
107 out[9] += (y[0]*n1[0] + y[1]*n1[1])*(1.0-20.0*qPos+90.0*pow(qPos,2)-140.0*pow(qPos,3)+70.0*pow(qPos,4))*it->weight()*sign1;
112 out[10] += (y[0]*n2[0] + y[1]*n2[1])*it->weight()*sign2;
113 out[11] += (y[0]*n2[0] + y[1]*n2[1])*(1.0 - 2.0*qPos)*it->weight();
114 out[12] += (y[0]*n2[0] + y[1]*n2[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign2;
115 out[13] += (y[0]*n2[0] + y[1]*n2[1])*(-20.0*qPos*qPos*qPos + 30.0*qPos*qPos - 12.0*qPos + 1.0)*it->weight();
116 out[14] += (y[0]*n2[0] + y[1]*n2[1])*(1.0-20.0*qPos+90.0*pow(qPos,2)-140.0*pow(qPos,3)+70.0*pow(qPos,4))*it->weight()*sign2;
121 out[15] += (y[0]*n3[0] + y[1]*n3[1])*it->weight()*sign3;
122 out[16] += (y[0]*n3[0] + y[1]*n3[1])*(2.0*qPos - 1.0)*it->weight();
123 out[17] += (y[0]*n3[0] + y[1]*n3[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign3;
124 out[18] += (y[0]*n3[0] + y[1]*n3[1])*(20.0*qPos*qPos*qPos - 30.0*qPos*qPos + 12.0*qPos - 1.0)*it->weight();
125 out[19] += (y[0]*n3[0] + y[1]*n3[1])*(1.0-20.0*qPos+90.0*pow(qPos,2)-140.0*pow(qPos,3)+70.0*pow(qPos,4))*it->weight()*sign3;
128 const QuadratureRule<Vector,2>& rule2 = QuadratureRules<Vector,2>::rule(GeometryTypes::cube(2), qOrder);
130 for (
typename QuadratureRule<Vector,2>::const_iterator it = rule2.begin();
131 it != rule2.end(); ++it)
133 FieldVector<double,2> qPos = it->position();
136 std::vector<std::vector<double> > l(2,std::vector<double> (5));
139 l[0][1]=2.0*qPos[0]-1.0;
140 l[1][1]=2.0*qPos[1]-1.0;
141 l[0][2]=6.0*qPos[0]*qPos[0]-6.0*qPos[0]+1.0;
142 l[1][2]=6.0*qPos[1]*qPos[1]-6.0*qPos[1]+1.0;
143 l[0][3]=20.0*qPos[0]*qPos[0]*qPos[0] - 30.0*qPos[0]*qPos[0] + 12.0*qPos[0] - 1.0;
144 l[1][3]=20.0*qPos[1]*qPos[1]*qPos[1] - 30.0*qPos[1]*qPos[1] + 12.0*qPos[1] - 1.0;
145 l[0][4]=1.0-20.0*qPos[0]+90.0*pow(qPos[0],2)-140.0*pow(qPos[0],3)+70.0*pow(qPos[0],4);
146 l[1][4]=1.0-20.0*qPos[1]+90.0*pow(qPos[1],2)-140.0*pow(qPos[1],3)+70.0*pow(qPos[1],4);
148 for (
int i=0;i<4;i++)
149 for (
int j=0;j<5;j++)
150 out[20+i*5+j] +=y[0]*l[0][i]*l[1][j]*it->weight();
152 for (
int i=0;i<5;i++)
153 for (
int j=0;j<4;j++)
154 out[40+i*4+j] +=y[1]*l[0][i]*l[1][j]*it->weight();
159 typename LB::Traits::RangeFieldType sign0, sign1, sign2, sign3;
160 typename LB::Traits::DomainType n0, n1, n2, n3;
Definition: bdfmcube.hh:16
Second order Raviart-Thomas shape functions on the reference triangle.
Definition: raviartthomas4cube2dlocalinterpolation.hh:24
RT4Cube2DLocalInterpolation(unsigned int s=0)
Make set number s, where 0 <= s < 16.
Definition: raviartthomas4cube2dlocalinterpolation.hh:33
void interpolate(const F &ff, std::vector< C > &out) const
Interpolate a given function with shape functions.
Definition: raviartthomas4cube2dlocalinterpolation.hh:72