3 #ifndef DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS2_CUBE2D_LOCALINTERPOLATION_HH 4 #define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS2_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);
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;
103 f.evaluate(localPos, y);
104 out[3] += (y[0]*n1[0] + y[1]*n1[1])*it->weight()*sign1;
105 out[4] += (y[0]*n1[0] + y[1]*n1[1])*(1.0 - 2.0*qPos)*it->weight();
106 out[5] += (y[0]*n1[0] + y[1]*n1[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign1;
110 f.evaluate(localPos, y);
111 out[6] += (y[0]*n2[0] + y[1]*n2[1])*it->weight()*sign2;
112 out[7] += (y[0]*n2[0] + y[1]*n2[1])*(1.0 - 2.0*qPos)*it->weight();
113 out[8] += (y[0]*n2[0] + y[1]*n2[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign2;
117 f.evaluate(localPos, y);
118 out[9] += (y[0]*n3[0] + y[1]*n3[1])*it->weight()*sign3;
119 out[10] += (y[0]*n3[0] + y[1]*n3[1])*(2.0*qPos - 1.0)*it->weight();
120 out[11] += (y[0]*n3[0] + y[1]*n3[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign3;
123 const QuadratureRule<Vector,2>& rule2 = QuadratureRules<Vector,2>::rule(GeometryType(GeometryType::cube,2), qOrder);
125 for (
typename QuadratureRule<Vector,2>::const_iterator it = rule2.begin();
126 it != rule2.end(); ++it)
128 FieldVector<double,2> qPos = it->position();
131 out[12] += y[0]*it->weight();
132 out[13] += y[1]*it->weight();
133 out[14] += y[0]*qPos[0]*it->weight();
134 out[15] += y[1]*qPos[0]*it->weight();
135 out[16] += y[0]*qPos[1]*it->weight();
136 out[17] += y[1]*qPos[1]*it->weight();
137 out[18] += y[0]*qPos[0]*qPos[1]*it->weight();
138 out[19] += y[1]*qPos[0]*qPos[1]*it->weight();
139 out[20] += y[0]*qPos[1]*qPos[1]*it->weight();
140 out[21] += y[1]*qPos[0]*qPos[0]*it->weight();
141 out[22] += y[0]*qPos[0]*qPos[1]*qPos[1]*it->weight();
142 out[23] += y[1]*qPos[0]*qPos[0]*qPos[1]*it->weight();
147 typename LB::Traits::RangeFieldType sign0, sign1, sign2, sign3;
148 typename LB::Traits::DomainType n0, n1, n2, n3;
151 #endif // DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS2_CUBE2D_LOCALINTERPOLATION_HH RT2Cube2DLocalInterpolation()
Standard constructor.
Definition: raviartthomas2cube2dlocalinterpolation.hh:27
Second order Raviart-Thomas shape functions on the reference triangle.
Definition: raviartthomas2cube2dlocalinterpolation.hh:22
Definition: brezzidouglasmarini1cube2dlocalbasis.hh:14
RT2Cube2DLocalInterpolation(unsigned int s)
Make set number s, where 0 <= s < 8.
Definition: raviartthomas2cube2dlocalinterpolation.hh:37
void interpolate(const F &f, std::vector< C > &out) const
Interpolate a given function with shape functions.
Definition: raviartthomas2cube2dlocalinterpolation.hh:76