Dune Core Modules (2.8.0)

brezzidouglasmarini2cube2dlocalinterpolation.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_BREZZIDOUGLASMARINI2_CUBE2D_LOCALINTERPOLATION_HH
4#define DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_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:
29 {
30 sign0 = sign1 = sign2 = sign3 = 1.0;
31 }
32
39 {
40 sign0 = sign1 = sign2 = sign3 = 1.0;
41 if (s & 1)
42 {
43 sign0 = -1.0;
44 }
45 if (s & 2)
46 {
47 sign1 = -1.0;
48 }
49 if (s & 4)
50 {
51 sign2 = -1.0;
52 }
53 if (s & 8)
54 {
55 sign3 = -1.0;
56 }
57
58 n0[0] = -1.0;
59 n0[1] = 0.0;
60 n1[0] = 1.0;
61 n1[1] = 0.0;
62 n2[0] = 0.0;
63 n2[1] = -1.0;
64 n3[0] = 0.0;
65 n3[1] = 1.0;
66 }
67
76 template<typename F, typename C>
77 void interpolate(const F& ff, std::vector<C>& out) const
78 {
79 // f gives v*outer normal at a point on the edge!
80 typedef typename LB::Traits::RangeFieldType Scalar;
81 typedef typename LB::Traits::DomainFieldType Vector;
82
83 auto&& f = Impl::makeFunctionWithCallOperator<typename LB::Traits::DomainType>(ff);
84
85 out.resize(14);
86 fill(out.begin(), out.end(), 0.0);
87
88 const int qOrder = 4;
90
91 for (typename QuadratureRule<Scalar,1>::const_iterator it = rule.begin();
92 it != rule.end(); ++it)
93 {
94 Scalar qPos = it->position();
95
96 typename LB::Traits::DomainType localPos;
97
98 localPos[0] = 0.0;
99 localPos[1] = qPos;
100 auto y = f(localPos);
101 out[0] += (y[0]*n0[0] + y[1]*n0[1])*it->weight()*sign0;
102 out[1] += (y[0]*n0[0] + y[1]*n0[1])*(2.0*qPos - 1.0)*it->weight();
103 out[2] += (y[0]*n0[0] + y[1]*n0[1])*(8.0*qPos*qPos - 8.0*qPos + 1.0)*it->weight()*sign0;
104
105 localPos[0] = 1.0;
106 localPos[1] = qPos;
107 y = f(localPos);
108 out[3] += (y[0]*n1[0]+y[1]*n1[1])*it->weight()*sign1;
109 out[4] += (y[0]*n1[0]+y[1]*n1[1])*(1.0 - 2.0*qPos)*it->weight();
110 out[5] += (y[0]*n1[0]+y[1]*n1[1])*(8.0*qPos*qPos - 8.0*qPos + 1.0)*it->weight()*sign1;
111
112 localPos[0] = qPos;
113 localPos[1] = 0.0;
114 y = f(localPos);
115 out[6] += (y[0]*n2[0] + y[1]*n2[1])*it->weight()*sign2;
116 out[7] += (y[0]*n2[0] + y[1]*n2[1])*(1.0 - 2.0*qPos)*it->weight();
117 out[8] += (y[0]*n2[0] + y[1]*n2[1])*(8.0*qPos*qPos - 8.0*qPos + 1.0)*it->weight()*sign2;
118
119 localPos[0] = qPos;
120 localPos[1] = 1.0;
121 y = f(localPos);
122 out[9] += (y[0]*n3[0] + y[1]*n3[1])*it->weight()*sign3;
123 out[10] += (y[0]*n3[0] + y[1]*n3[1])*(2.0*qPos - 1.0)*it->weight();
124 out[11] += (y[0]*n3[0] + y[1]*n3[1])*(8.0*qPos*qPos - 8.0*qPos + 1.0)*it->weight()*sign3;
125 }
126
128
129 for (typename QuadratureRule<Vector,2>::const_iterator it=rule2.begin(); it!=rule2.end(); ++it)
130 {
131 auto y = f(it->position());
132 out[12] += y[0]*it->weight();
133 out[13] += y[1]*it->weight();
134 }
135 }
136
137 private:
138 typename LB::Traits::RangeFieldType sign0, sign1, sign2, sign3;
139 typename LB::Traits::DomainType n0, n1, n2, n3;
140 };
141} // end namespace Dune
142#endif // DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_CUBE2D_LOCALINTERPOLATION_HH
First order Brezzi-Douglas-Marini shape functions on quadrilaterals.
Definition: brezzidouglasmarini2cube2dlocalinterpolation.hh:24
BDM2Cube2DLocalInterpolation(unsigned int s)
Make set number s, where 0 <= s < 16.
Definition: brezzidouglasmarini2cube2dlocalinterpolation.hh:38
BDM2Cube2DLocalInterpolation()
Standard constructor.
Definition: brezzidouglasmarini2cube2dlocalinterpolation.hh:28
void interpolate(const F &ff, std::vector< C > &out) const
Interpolate a given function with shape functions.
Definition: brezzidouglasmarini2cube2dlocalinterpolation.hh:77
Abstract base class for quadrature rules.
Definition: quadraturerules.hh:152
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
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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