3 #ifndef DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS4_CUBE2D_LOCALINTERPOLATION_HH 4 #define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS4_CUBE2D_LOCALINTERPOLATION_HH 8 #include <dune/geometry/quadraturerules.hh> 29 sign0 = sign1 = sign2 = sign3 = 1.0;
39 sign0 = sign1 = sign2 = sign3 = 1.0;
75 template<
typename F,
typename C>
79 typedef typename LB::Traits::RangeFieldType Scalar;
80 typedef typename LB::Traits::DomainFieldType Vector;
81 typename F::Traits::RangeType y;
84 fill(out.begin(), out.end(), 0.0);
86 const int qOrder = 12;
87 const QuadratureRule<Scalar,1>& rule = QuadratureRules<Scalar,1>::rule(GeometryType(GeometryType::cube,1), qOrder);
89 for (
typename QuadratureRule<Scalar,1>::const_iterator it=rule.begin(); it!=rule.end(); ++it)
91 Scalar qPos = it->position();
92 typename LB::Traits::DomainType localPos;
96 f.evaluate(localPos, y);
97 out[0] += (y[0]*n0[0] + y[1]*n0[1])*it->weight()*sign0;
98 out[1] += (y[0]*n0[0] + y[1]*n0[1])*(2.0*qPos - 1.0)*it->weight();
99 out[2] += (y[0]*n0[0] + y[1]*n0[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign0;
100 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();
101 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;
105 f.evaluate(localPos, y);
106 out[5] += (y[0]*n1[0] + y[1]*n1[1])*it->weight()*sign1;
107 out[6] += (y[0]*n1[0] + y[1]*n1[1])*(1.0 - 2.0*qPos)*it->weight();
108 out[7] += (y[0]*n1[0] + y[1]*n1[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign1;
109 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();
110 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;
114 f.evaluate(localPos, y);
115 out[10] += (y[0]*n2[0] + y[1]*n2[1])*it->weight()*sign2;
116 out[11] += (y[0]*n2[0] + y[1]*n2[1])*(1.0 - 2.0*qPos)*it->weight();
117 out[12] += (y[0]*n2[0] + y[1]*n2[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign2;
118 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();
119 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;
123 f.evaluate(localPos, y);
124 out[15] += (y[0]*n3[0] + y[1]*n3[1])*it->weight()*sign3;
125 out[16] += (y[0]*n3[0] + y[1]*n3[1])*(2.0*qPos - 1.0)*it->weight();
126 out[17] += (y[0]*n3[0] + y[1]*n3[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign3;
127 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();
128 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;
131 const QuadratureRule<Vector,2>& rule2 = QuadratureRules<Vector,2>::rule(GeometryType(GeometryType::cube,2), qOrder);
133 for (
typename QuadratureRule<Vector,2>::const_iterator it = rule2.begin();
134 it != rule2.end(); ++it)
136 FieldVector<double,2> qPos = it->position();
139 std::vector<std::vector<double> > l(2,std::vector<double> (5));
142 l[0][1]=2.0*qPos[0]-1.0;
143 l[1][1]=2.0*qPos[1]-1.0;
144 l[0][2]=6.0*qPos[0]*qPos[0]-6.0*qPos[0]+1.0;
145 l[1][2]=6.0*qPos[1]*qPos[1]-6.0*qPos[1]+1.0;
146 l[0][3]=20.0*qPos[0]*qPos[0]*qPos[0] - 30.0*qPos[0]*qPos[0] + 12.0*qPos[0] - 1.0;
147 l[1][3]=20.0*qPos[1]*qPos[1]*qPos[1] - 30.0*qPos[1]*qPos[1] + 12.0*qPos[1] - 1.0;
148 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);
149 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);
151 for (
int i=0;i<4;i++)
152 for (
int j=0;j<5;j++)
153 out[20+i*5+j] +=y[0]*l[0][i]*l[1][j]*it->weight();
155 for (
int i=0;i<5;i++)
156 for (
int j=0;j<4;j++)
157 out[40+i*4+j] +=y[1]*l[0][i]*l[1][j]*it->weight();
162 typename LB::Traits::RangeFieldType sign0, sign1, sign2, sign3;
163 typename LB::Traits::DomainType n0, n1, n2, n3;
167 #endif // DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS3_CUBE2D_LOCALINTERPOLATION_HH Second order Raviart-Thomas shape functions on the reference triangle.
Definition: raviartthomas4cube2dlocalinterpolation.hh:22
Definition: brezzidouglasmarini1cube2dlocalbasis.hh:15
RT4Cube2DLocalInterpolation()
Standard constructor.
Definition: raviartthomas4cube2dlocalinterpolation.hh:27
RT4Cube2DLocalInterpolation(unsigned int s)
Make set number s, where 0 <= s < 8.
Definition: raviartthomas4cube2dlocalinterpolation.hh:37
void interpolate(const F &f, std::vector< C > &out) const
Interpolate a given function with shape functions.
Definition: raviartthomas4cube2dlocalinterpolation.hh:76