DUNE-FEM (unstable)

brezzidouglasmarini2simplex2dlocalinterpolation.hh
1// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
2// vi: set et ts=4 sw=2 sts=2:
3// SPDX-FileCopyrightInfo: Copyright © DUNE Project contributors, see file LICENSE.md in module root
4// SPDX-License-Identifier: LicenseRef-GPL-2.0-only-with-DUNE-exception
5#ifndef DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_SIMPLEX2D_LOCALINTERPOLATION_HH
6#define DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_SIMPLEX2D_LOCALINTERPOLATION_HH
7
8#include <vector>
9
11
12namespace Dune
13{
14
23 template<class LB>
25 {
26
27 public:
30 {
31 sign0 = sign1 = sign2 = 1.0;
32 }
33
40 {
41 sign0 = sign1 = sign2 = 1.0;
42 if (s & 1)
43 {
44 sign0 = -1.0;
45 }
46 if (s & 2)
47 {
48 sign1 = -1.0;
49 }
50 if (s & 4)
51 {
52 sign2 = -1.0;
53 }
54
55 m0[0] = 0.5;
56 m0[1] = 0.0;
57 m1[0] = 0.0;
58 m1[1] = 0.5;
59 m2[0] = 0.5;
60 m2[1] = 0.5;
61 n0[0] = 0.0;
62 n0[1] = -1.0;
63 n1[0] = -1.0;
64 n1[1] = 0.0;
65 n2[0] = 1.0/sqrt(2.0);
66 n2[1] = 1.0/sqrt(2.0);
67 c0 = 0.5*n0[0] - 1.0*n0[1];
68 c1 = -1.0*n1[0] + 0.5*n1[1];
69 c2 = 0.5*n2[0] + 0.5*n2[1];
70 }
71
80 template<typename F, typename C>
81 void interpolate(const F& f, std::vector<C>& out) const
82 {
83 // f gives v*outer normal at a point on the edge!
84 typedef typename LB::Traits::RangeFieldType Scalar;
85 typedef typename LB::Traits::DomainFieldType Vector;
86
87 out.resize(12);
88 fill(out.begin(), out.end(), 0.0);
89
90 const int qOrder = 4;
92
93 for (typename Dune::QuadratureRule<Scalar,1>::const_iterator it=rule.begin(); it!=rule.end(); ++it)
94 {
95 Scalar qPos = it->position();
96
97 typename LB::Traits::DomainType localPos;
98
99 localPos[0] = qPos;
100 localPos[1] = 0.0;
101 auto y = f(localPos);
102 out[0] += (y[0]*n0[0] + y[1]*n0[1])*it->weight()*sign0/c0;
103 out[1] += (y[0]*n0[0] + y[1]*n0[1])*(1.0 - 2.0*qPos)*it->weight()/c0;
104 out[2] += (y[0]*n0[0] + y[1]*n0[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign0/c0;
105
106 localPos[0] = 0.0;
107 localPos[1] = qPos;
108 y = f(localPos);
109 out[3] += (y[0]*n1[0]+y[1]*n1[1])*it->weight()*sign1/c1;
110 out[4] += (y[0]*n1[0]+y[1]*n1[1])*(2.0*qPos-1.0)*it->weight()/c1;
111 out[5] += (y[0]*n1[0]+y[1]*n1[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign1/c1;
112
113 localPos[0] = 1.0 - qPos;
114 localPos[1] = qPos;
115 y = f(localPos);
116 out[6] += (y[0]*n2[0] + y[1]*n2[1])*it->weight()*sign2/c2;
117 out[7] += (y[0]*n2[0] + y[1]*n2[1])*(1.0 - 2.0*qPos)*it->weight()/c2;
118 out[8] += (y[0]*n2[0] + y[1]*n2[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign2/c2;
119 }
120
121 // a volume part is needed here for dofs: 9 10 11
123
124 for (typename QuadratureRule<Vector,2>::const_iterator it=rule2.begin(); it!=rule2.end(); ++it)
125 {
126 typename LB::Traits::DomainType localPos = it->position();
127 auto y = f(localPos);
128
129 out[9] += y[0]*it->weight();
130 out[10] += y[1]*it->weight();
131 out[11] += (y[0]*(localPos[0]-2.0*localPos[0]*localPos[1]-localPos[0]*localPos[0])
132 +y[1]*(-localPos[1]+2.0*localPos[0]*localPos[1]+localPos[1]*localPos[1]))*it->weight();
133 }
134 }
135
136 private:
137 typename LB::Traits::RangeFieldType sign0, sign1, sign2;
138 typename LB::Traits::DomainType m0, m1, m2;
139 typename LB::Traits::DomainType n0, n1, n2;
140 typename LB::Traits::RangeFieldType c0, c1, c2;
141 };
142} // end namespace Dune
143#endif // DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_SIMPLEX2D_LOCALINTERPOLATION_HH
First order Brezzi-Douglas-Marini shape functions on triangles.
Definition: brezzidouglasmarini2simplex2dlocalinterpolation.hh:25
BDM2Simplex2DLocalInterpolation()
Standard constructor.
Definition: brezzidouglasmarini2simplex2dlocalinterpolation.hh:29
void interpolate(const F &f, std::vector< C > &out) const
Interpolate a given function with shape functions.
Definition: brezzidouglasmarini2simplex2dlocalinterpolation.hh:81
BDM2Simplex2DLocalInterpolation(unsigned int s)
Make set number s, where 0 <= s < 8.
Definition: brezzidouglasmarini2simplex2dlocalinterpolation.hh:39
Abstract base class for quadrature rules.
Definition: quadraturerules.hh:214
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:326
constexpr GeometryType simplex(unsigned int dim)
Returns a GeometryType representing a simplex of dimension dim.
Definition: type.hh:453
typename Overloads::ScalarType< std::decay_t< V > >::type Scalar
Element type of some SIMD type.
Definition: interface.hh:235
Dune namespace.
Definition: alignedallocator.hh:13
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