Dune Core Modules (2.8.0)

raviartthomas3cube2dlocalinterpolation.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_RAVIARTTHOMAS3_CUBE2D_LOCALINTERPOLATION_HH
4#define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS3_CUBE2D_LOCALINTERPOLATION_HH
5
6#include <vector>
7
9#include <dune/localfunctions/common/localinterpolation.hh>
10
11namespace Dune
12{
13
22 template<class LB>
24 {
25
26 public:
27
33 RT3Cube2DLocalInterpolation (std::bitset<4> s = 0)
34 {
35 for (size_t i=0; i<4; i++)
36 sign_[i] = (s[i]) ? -1.0 : 1.0;
37
38 n_[0] = {-1.0, 0.0};
39 n_[1] = { 1.0, 0.0};
40 n_[2] = { 0.0, -1.0};
41 n_[3] = { 0.0, 1.0};
42 }
43
52 template<typename F, typename C>
53 void interpolate (const F& ff, std::vector<C>& out) const
54 {
55 // f gives v*outer normal at a point on the edge!
56 typedef typename LB::Traits::RangeFieldType Scalar;
57 typedef typename LB::Traits::DomainFieldType Vector;
58
59 auto&& f = Impl::makeFunctionWithCallOperator<typename LB::Traits::DomainType>(ff);
60
61 out.resize(40);
62 fill(out.begin(), out.end(), 0.0);
63
64 const int qOrder = 9;
65 const auto& rule1 = QuadratureRules<Scalar,1>::rule(GeometryTypes::cube(1), qOrder);
66
67 for (auto&& qp : rule1)
68 {
69 Scalar qPos = qp.position();
70 typename LB::Traits::DomainType localPos;
71
72 localPos = {0.0, qPos};
73 auto y = f(localPos);
74 out[0] += (y[0]*n_[0][0] + y[1]*n_[0][1])*qp.weight()*sign_[0];
75 out[1] += (y[0]*n_[0][0] + y[1]*n_[0][1])*(2.0*qPos - 1.0)*qp.weight();
76 out[2] += (y[0]*n_[0][0] + y[1]*n_[0][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[0];
77 out[3] += (y[0]*n_[0][0] + y[1]*n_[0][1])*(20.0*qPos*qPos*qPos - 30.0*qPos*qPos + 12.0*qPos - 1.0)*qp.weight();
78
79 localPos = {1.0, qPos};
80 y = f(localPos);
81 out[4] += (y[0]*n_[1][0] + y[1]*n_[1][1])*qp.weight()*sign_[1];
82 out[5] += (y[0]*n_[1][0] + y[1]*n_[1][1])*(1.0 - 2.0*qPos)*qp.weight();
83 out[6] += (y[0]*n_[1][0] + y[1]*n_[1][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[1];
84 out[7] += (y[0]*n_[1][0] + y[1]*n_[1][1])*(-20.0*qPos*qPos*qPos + 30.0*qPos*qPos - 12.0*qPos + 1.0)*qp.weight();
85
86 localPos = {qPos, 0.0};
87 y = f(localPos);
88 out[8] += (y[0]*n_[2][0] + y[1]*n_[2][1])*qp.weight()*sign_[2];
89 out[9] += (y[0]*n_[2][0] + y[1]*n_[2][1])*(1.0 - 2.0*qPos)*qp.weight();
90 out[10] += (y[0]*n_[2][0] + y[1]*n_[2][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[2];
91 out[11] += (y[0]*n_[2][0] + y[1]*n_[2][1])*(-20.0*qPos*qPos*qPos + 30.0*qPos*qPos - 12.0*qPos + 1.0)*qp.weight();
92
93 localPos = {qPos, 1.0};
94 y = f(localPos);
95 out[12] += (y[0]*n_[3][0] + y[1]*n_[3][1])*qp.weight()*sign_[3];
96 out[13] += (y[0]*n_[3][0] + y[1]*n_[3][1])*(2.0*qPos - 1.0)*qp.weight();
97 out[14] += (y[0]*n_[3][0] + y[1]*n_[3][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[3];
98 out[15] += (y[0]*n_[3][0] + y[1]*n_[3][1])*(20.0*qPos*qPos*qPos - 30.0*qPos*qPos + 12.0*qPos - 1.0)*qp.weight();
99 }
100
101 const auto& rule2 = QuadratureRules<Vector,2>::rule(GeometryTypes::cube(2), qOrder);
102
103 for (auto&& qp : rule2)
104 {
105 auto qPos = qp.position();
106
107 auto y = f(qPos);
108 double l0_x=1.0;
109 double l1_x=2.0*qPos[0]-1.0;
110 double l2_x=6.0*qPos[0]*qPos[0]-6.0*qPos[0]+1.0;
111 double l3_x=20.0*qPos[0]*qPos[0]*qPos[0] - 30.0*qPos[0]*qPos[0] + 12.0*qPos[0] - 1.0;
112 double l0_y=1.0;
113 double l1_y=2.0*qPos[1]-1.0;
114 double l2_y=6.0*qPos[1]*qPos[1]-6.0*qPos[1]+1.0;
115 double l3_y=20.0*qPos[1]*qPos[1]*qPos[1] - 30.0*qPos[1]*qPos[1] + 12.0*qPos[1] - 1.0;
116
117 out[16] += y[0]*l0_x*l0_y*qp.weight();
118 out[17] += y[0]*l0_x*l1_y*qp.weight();
119 out[18] += y[0]*l0_x*l2_y*qp.weight();
120 out[19] += y[0]*l0_x*l3_y*qp.weight();
121 out[20] += y[0]*l1_x*l0_y*qp.weight();
122 out[21] += y[0]*l1_x*l1_y*qp.weight();
123 out[22] += y[0]*l1_x*l2_y*qp.weight();
124 out[23] += y[0]*l1_x*l3_y*qp.weight();
125 out[24] += y[0]*l2_x*l0_y*qp.weight();
126 out[25] += y[0]*l2_x*l1_y*qp.weight();
127 out[26] += y[0]*l2_x*l2_y*qp.weight();
128 out[27] += y[0]*l2_x*l3_y*qp.weight();
129
130 out[28] += y[1]*l0_x*l0_y*qp.weight();
131 out[29] += y[1]*l0_x*l1_y*qp.weight();
132 out[30] += y[1]*l0_x*l2_y*qp.weight();
133 out[31] += y[1]*l1_x*l0_y*qp.weight();
134 out[32] += y[1]*l1_x*l1_y*qp.weight();
135 out[33] += y[1]*l1_x*l2_y*qp.weight();
136 out[34] += y[1]*l2_x*l0_y*qp.weight();
137 out[35] += y[1]*l2_x*l1_y*qp.weight();
138 out[36] += y[1]*l2_x*l2_y*qp.weight();
139 out[37] += y[1]*l3_x*l0_y*qp.weight();
140 out[38] += y[1]*l3_x*l1_y*qp.weight();
141 out[39] += y[1]*l3_x*l2_y*qp.weight();
142 }
143 }
144
145 private:
146 // Edge orientations
147 std::array<typename LB::Traits::RangeFieldType, 4> sign_;
148
149 // Edge normals
150 std::array<typename LB::Traits::DomainType, 4> n_;
151 };
152}
153
154#endif // DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS3_CUBE2D_LOCALINTERPOLATION_HH
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
Second order Raviart-Thomas shape functions on the reference quadrilateral.
Definition: raviartthomas3cube2dlocalinterpolation.hh:24
RT3Cube2DLocalInterpolation(std::bitset< 4 > s=0)
Make set number s, where 0 <= s < 16.
Definition: raviartthomas3cube2dlocalinterpolation.hh:33
void interpolate(const F &ff, std::vector< C > &out) const
Interpolate a given function with shape functions.
Definition: raviartthomas3cube2dlocalinterpolation.hh:53
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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