Dune Core Modules (2.8.0)

raviartthomas1cube3dlocalinterpolation.hh
1// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
2// vi: set et ts=4 sw=2 sts=2:
3#ifndef DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS1_CUBE3D_LOCALINTERPOLATION_HH
4#define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS1_CUBE3D_LOCALINTERPOLATION_HH
5
6#include <vector>
7
9#include <dune/localfunctions/common/localinterpolation.hh>
10
11namespace Dune
12{
21 template<class LB>
23 {
24
25 public:
26
32 RT1Cube3DLocalInterpolation (std::bitset<6> s = 0)
33 {
34 for (size_t i=0; i<6; i++)
35 sign_[i] = (s[i]) ? -1.0 : 1.0;
36
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};
43 }
44
53 template<class F, class C>
54 void interpolate (const F& ff, std::vector<C>& out) const
55 {
56 // f gives v*outer normal at a point on the edge!
57 typedef typename LB::Traits::RangeFieldType Scalar;
58 typedef typename LB::Traits::DomainFieldType Vector;
59
60 auto&& f = Impl::makeFunctionWithCallOperator<typename LB::Traits::DomainType>(ff);
61
62 out.resize(36);
63 fill(out.begin(), out.end(), 0.0);
64
65 const int qOrder = 3;
66 const auto& rule1 = QuadratureRules<Scalar,2>::rule(GeometryTypes::cube(2), qOrder);
67
68 for (auto&& qp : rule1)
69 {
70 Dune::FieldVector<Scalar,2> qPos = qp.position();
71 typename LB::Traits::DomainType localPos;
72
73 localPos = {0.0, qPos[0], qPos[1]};
74 auto y = f(localPos);
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();
79
80 localPos = {1.0, qPos[0], qPos[1]};
81 y = f(localPos);
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();
86
87 localPos = {qPos[0], 0.0, qPos[1]};
88 y = f(localPos);
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();
93
94 localPos = {qPos[0], 1.0, qPos[1]};
95 y = f(localPos);
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();
100
101 localPos = {qPos[0], qPos[1], 0.0};
102 y = f(localPos);
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();
107
108 localPos = {qPos[0], qPos[1], 1.0};
109 y = f(localPos);
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();
114 }
115
116 const auto& rule2 = QuadratureRules<Vector,3>::rule(GeometryTypes::cube(3), qOrder);
117 for (auto&& qp : rule2)
118 {
119 FieldVector<double,3> qPos = qp.position();
120
121 auto y = f(qPos);
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();
134 }
135 }
136
137 private:
138 // Facet orientations
139 std::array<typename LB::Traits::RangeFieldType, 6> sign_;
140
141 // Facet normals
142 std::array<typename LB::Traits::DomainType, 6> n_;
143 };
144}
145#endif // DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS1_CUBE3D_LOCALINTERPOLATION_HH
vector space out of a tensor product of fields.
Definition: fvector.hh:95
static const QuadratureRule & rule(const GeometryType &t, int p, QuadratureType::Enum qt=QuadratureType::GaussLegendre)
select the appropriate QuadratureRule for GeometryType t and order p
Definition: quadraturerules.hh:280
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
constexpr GeometryType cube(unsigned int dim)
Returns a GeometryType representing a hypercube of dimension dim.
Definition: type.hh:470
typename Overloads::ScalarType< std::decay_t< V > >::type Scalar
Element type of some SIMD type.
Definition: interface.hh:233
Dune namespace.
Definition: alignedallocator.hh:11
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