3 #ifndef DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_SIMPLEX2D_LOCALINTERPOLATION_HH
4 #define DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_SIMPLEX2D_LOCALINTERPOLATION_HH
8 #include <dune/geometry/quadraturerules.hh>
29 sign0 = sign1 = sign2 = 1.0;
39 sign0 = sign1 = sign2 = 1.0;
63 n2[0] = 1.0/sqrt(2.0);
64 n2[1] = 1.0/sqrt(2.0);
65 c0 = 0.5*n0[0] - 1.0*n0[1];
66 c1 = -1.0*n1[0] + 0.5*n1[1];
67 c2 = 0.5*n2[0] + 0.5*n2[1];
78 template<
typename F,
typename C>
82 typedef typename LB::Traits::RangeFieldType Scalar;
83 typedef typename LB::Traits::DomainFieldType Vector;
84 typename F::Traits::RangeType y;
87 fill(out.begin(), out.end(), 0.0);
90 const Dune::QuadratureRule<Scalar,1>& rule = Dune::QuadratureRules<Scalar,1>::rule(Dune::GeometryTypes::simplex(1), qOrder);
92 for (
typename Dune::QuadratureRule<Scalar,1>::const_iterator it=rule.begin(); it!=rule.end(); ++it)
94 Scalar qPos = it->position();
96 typename LB::Traits::DomainType localPos;
100 f.evaluate(localPos, y);
101 out[0] += (y[0]*n0[0] + y[1]*n0[1])*it->weight()*sign0/c0;
102 out[1] += (y[0]*n0[0] + y[1]*n0[1])*(1.0 - 2.0*qPos)*it->weight()/c0;
103 out[2] += (y[0]*n0[0] + y[1]*n0[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign0/c0;
107 f.evaluate(localPos, y);
108 out[3] += (y[0]*n1[0]+y[1]*n1[1])*it->weight()*sign1/c1;
109 out[4] += (y[0]*n1[0]+y[1]*n1[1])*(2.0*qPos-1.0)*it->weight()/c1;
110 out[5] += (y[0]*n1[0]+y[1]*n1[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign1/c1;
112 localPos[0] = 1.0 - qPos;
114 f.evaluate(localPos, y);
115 out[6] += (y[0]*n2[0] + y[1]*n2[1])*it->weight()*sign2/c2;
116 out[7] += (y[0]*n2[0] + y[1]*n2[1])*(1.0 - 2.0*qPos)*it->weight()/c2;
117 out[8] += (y[0]*n2[0] + y[1]*n2[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign2/c2;
121 const QuadratureRule<Vector,2>& rule2 = QuadratureRules<Vector,2>::rule(GeometryTypes::simplex(2), qOrder);
123 for (
typename QuadratureRule<Vector,2>::const_iterator it=rule2.begin(); it!=rule2.end(); ++it)
125 typename LB::Traits::DomainType localPos = it->position();
126 f.evaluate(localPos, y);
128 out[9] += y[0]*it->weight();
129 out[10] += y[1]*it->weight();
130 out[11] += (y[0]*(localPos[0]-2.0*localPos[0]*localPos[1]-localPos[0]*localPos[0])
131 +y[1]*(-localPos[1]+2.0*localPos[0]*localPos[1]+localPos[1]*localPos[1]))*it->weight();
136 typename LB::Traits::RangeFieldType sign0, sign1, sign2;
137 typename LB::Traits::DomainType m0, m1, m2;
138 typename LB::Traits::DomainType n0, n1, n2;
139 typename LB::Traits::RangeFieldType c0, c1, c2;
142 #endif // DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_SIMPLEX2D_LOCALINTERPOLATION_HH