3 #ifndef DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS1_CUBE3D_LOCALINTERPOLATION_HH
4 #define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS1_CUBE3D_LOCALINTERPOLATION_HH
8 #include <dune/geometry/quadraturerules.hh>
34 for (
size_t i=0; i<6; i++)
35 sign_[i] = (s[i]) ? -1.0 : 1.0;
37 n_[0] = {-1.0, 0.0, 0.0};
38 n_[1] = { 1.0, 0.0, 0.0};
39 n_[2] = { 0.0, -1.0, 0.0};
40 n_[3] = { 0.0, 1.0, 0.0};
41 n_[4] = { 0.0, 0.0, -1.0};
42 n_[5] = { 0.0, 0.0, 1.0};
53 template<
class F,
class C>
57 typedef typename LB::Traits::RangeFieldType Scalar;
58 typedef typename LB::Traits::DomainFieldType Vector;
60 auto&& f = Impl::makeFunctionWithCallOperator<typename LB::Traits::DomainType>(ff);
63 fill(out.begin(), out.end(), 0.0);
66 const auto& rule1 = QuadratureRules<Scalar,2>::rule(GeometryTypes::cube(2), qOrder);
68 for (
auto&& qp : rule1)
70 Dune::FieldVector<Scalar,2> qPos = qp.position();
71 typename LB::Traits::DomainType localPos;
73 localPos = {0.0, qPos[0], qPos[1]};
75 out[0] += (y[0]*n_[0][0] + y[1]*n_[0][1] + y[2]*n_[0][2])*qp.weight()*sign_[0];
76 out[6] += (y[0]*n_[0][0] + y[1]*n_[0][1] + y[2]*n_[0][2])*(2.0*qPos[0] - 1.0)*qp.weight();
77 out[12] += (y[0]*n_[0][0] + y[1]*n_[0][1] + y[2]*n_[0][2])*(2.0*qPos[1] - 1.0)*qp.weight();
78 out[18] += (y[0]*n_[0][0] + y[1]*n_[0][1] + y[2]*n_[0][2])*(2.0*qPos[0] - 1.0)*(2.0*qPos[1] - 1.0)*qp.weight();
80 localPos = {1.0, qPos[0], qPos[1]};
82 out[1] += (y[0]*n_[1][0] + y[1]*n_[1][1] + y[2]*n_[1][2])*qp.weight()*sign_[1];
83 out[7] += (y[0]*n_[1][0] + y[1]*n_[1][1] + y[2]*n_[1][2])*(1.0 - 2.0*qPos[0])*qp.weight();
84 out[13] += (y[0]*n_[1][0] + y[1]*n_[1][1] + y[2]*n_[1][2])*(1.0 - 2.0*qPos[1])*qp.weight();
85 out[19] += (y[0]*n_[1][0] + y[1]*n_[1][1] + y[2]*n_[1][2])*(1.0 - 2.0*qPos[0])*(2.0*qPos[1] - 1.0)*qp.weight();
87 localPos = {qPos[0], 0.0, qPos[1]};
89 out[2] += (y[0]*n_[2][0] + y[1]*n_[2][1] + y[2]*n_[2][2])*qp.weight()*sign_[2];
90 out[8] += (y[0]*n_[2][0] + y[1]*n_[2][1] + y[2]*n_[2][2])*(1.0 - 2.0*qPos[0])*qp.weight();
91 out[14] += (y[0]*n_[2][0] + y[1]*n_[2][1] + y[2]*n_[2][2])*(2.0*qPos[1] - 1.0)*qp.weight();
92 out[20] += (y[0]*n_[2][0] + y[1]*n_[2][1] + y[2]*n_[2][2])*(1.0 - 2.0*qPos[0])*(2.0*qPos[1] - 1.0)*qp.weight();
94 localPos = {qPos[0], 1.0, qPos[1]};
96 out[3] += (y[0]*n_[3][0] + y[1]*n_[3][1] + y[2]*n_[3][2])*qp.weight()*sign_[3];
97 out[9] += (y[0]*n_[3][0] + y[1]*n_[3][1] + y[2]*n_[3][2])*(2.0*qPos[0] - 1.0)*qp.weight();
98 out[15] += (y[0]*n_[3][0] + y[1]*n_[3][1] + y[2]*n_[3][2])*(1.0 - 2.0*qPos[1])*qp.weight();
99 out[21] += (y[0]*n_[3][0] + y[1]*n_[3][1] + y[2]*n_[3][2])*(2.0*qPos[0] - 1.0)*(2.0*qPos[1] - 1.0)*qp.weight();
101 localPos = {qPos[0], qPos[1], 0.0};
103 out[4] += (y[0]*n_[4][0] + y[1]*n_[4][1] + y[2]*n_[4][2])*qp.weight()*sign_[4];
104 out[10] += (y[0]*n_[4][0] + y[1]*n_[4][1] + y[2]*n_[4][2])*(1.0 - 2.0*qPos[0])*qp.weight();
105 out[16] += (y[0]*n_[4][0] + y[1]*n_[4][1] + y[2]*n_[4][2])*(1.0 - 2.0*qPos[1])*qp.weight();
106 out[22] += (y[0]*n_[4][0] + y[1]*n_[4][1] + y[2]*n_[4][2])*(1.0 - 2.0*qPos[0])*(2.0*qPos[1] - 1.0)*qp.weight();
108 localPos = {qPos[0], qPos[1], 1.0};
110 out[5] += (y[0]*n_[5][0] + y[1]*n_[5][1] + y[2]*n_[5][2])*qp.weight()*sign_[5];
111 out[11] += (y[0]*n_[5][0] + y[1]*n_[5][1] + y[2]*n_[5][2])*(2.0*qPos[0] - 1.0)*qp.weight();
112 out[17] += (y[0]*n_[5][0] + y[1]*n_[5][1] + y[2]*n_[5][2])*(2.0*qPos[1] - 1.0)*qp.weight();
113 out[23] += (y[0]*n_[5][0] + y[1]*n_[5][1] + y[2]*n_[5][2])*(2.0*qPos[0] - 1.0)*(2.0*qPos[1] - 1.0)*qp.weight();
116 const auto& rule2 = QuadratureRules<Vector,3>::rule(GeometryTypes::cube(3), qOrder);
117 for (
auto&& qp : rule2)
119 FieldVector<double,3> qPos = qp.position();
122 out[24] += y[0]*qp.weight();
123 out[25] += y[1]*qp.weight();
124 out[26] += y[2]*qp.weight();
125 out[27] += y[0]*qPos[1]*qp.weight();
126 out[28] += y[0]*qPos[2]*qp.weight();
127 out[29] += y[1]*qPos[0]*qp.weight();
128 out[30] += y[1]*qPos[2]*qp.weight();
129 out[31] += y[2]*qPos[0]*qp.weight();
130 out[32] += y[2]*qPos[1]*qp.weight();
131 out[33] += y[0]*qPos[1]*qPos[2]*qp.weight();
132 out[34] += y[1]*qPos[0]*qPos[2]*qp.weight();
133 out[35] += y[2]*qPos[0]*qPos[1]*qp.weight();
139 std::array<typename LB::Traits::RangeFieldType, 6> sign_;
142 std::array<typename LB::Traits::DomainType, 6> n_;
Definition: bdfmcube.hh:16
First order Raviart-Thomas shape functions on the reference hexahedron.
Definition: raviartthomas1cube3dlocalinterpolation.hh:23
void interpolate(const F &ff, std::vector< C > &out) const
Interpolate a given function with shape functions.
Definition: raviartthomas1cube3dlocalinterpolation.hh:54
RT1Cube3DLocalInterpolation(std::bitset< 6 > s=0)
Make set number s, where 0 <= s < 64.
Definition: raviartthomas1cube3dlocalinterpolation.hh:32