Dune Core Modules (2.7.0)

raviartthomas4cube2dlocalinterpolation.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_RAVIARTTHOMAS4_CUBE2D_LOCALINTERPOLATION_HH
4#define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS4_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(60);
86 fill(out.begin(), out.end(), 0.0);
87
88 const int qOrder = 12;
90
91 for (typename QuadratureRule<Scalar,1>::const_iterator it=rule.begin(); it!=rule.end(); ++it)
92 {
93 Scalar qPos = it->position();
94 typename LB::Traits::DomainType localPos;
95
96 localPos[0] = 0.0;
97 localPos[1] = qPos;
98 auto y = f(localPos);
99 out[0] += (y[0]*n0[0] + y[1]*n0[1])*it->weight()*sign0;
100 out[1] += (y[0]*n0[0] + y[1]*n0[1])*(2.0*qPos - 1.0)*it->weight();
101 out[2] += (y[0]*n0[0] + y[1]*n0[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign0;
102 out[3] += (y[0]*n0[0] + y[1]*n0[1])*(20.0*qPos*qPos*qPos - 30.0*qPos*qPos + 12.0*qPos - 1.0)*it->weight();
103 out[4] += (y[0]*n0[0] + y[1]*n0[1])*(1.0-20.0*qPos+90.0*pow(qPos,2)-140.0*pow(qPos,3)+70.0*pow(qPos,4))*it->weight()*sign0;
104
105 localPos[0] = 1.0;
106 localPos[1] = qPos;
107 y = f(localPos);
108 out[5] += (y[0]*n1[0] + y[1]*n1[1])*it->weight()*sign1;
109 out[6] += (y[0]*n1[0] + y[1]*n1[1])*(1.0 - 2.0*qPos)*it->weight();
110 out[7] += (y[0]*n1[0] + y[1]*n1[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign1;
111 out[8] += (y[0]*n1[0] + y[1]*n1[1])*(-20.0*qPos*qPos*qPos + 30.0*qPos*qPos - 12.0*qPos + 1.0)*it->weight();
112 out[9] += (y[0]*n1[0] + y[1]*n1[1])*(1.0-20.0*qPos+90.0*pow(qPos,2)-140.0*pow(qPos,3)+70.0*pow(qPos,4))*it->weight()*sign1;
113
114 localPos[0] = qPos;
115 localPos[1] = 0.0;
116 y = f(localPos);
117 out[10] += (y[0]*n2[0] + y[1]*n2[1])*it->weight()*sign2;
118 out[11] += (y[0]*n2[0] + y[1]*n2[1])*(1.0 - 2.0*qPos)*it->weight();
119 out[12] += (y[0]*n2[0] + y[1]*n2[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign2;
120 out[13] += (y[0]*n2[0] + y[1]*n2[1])*(-20.0*qPos*qPos*qPos + 30.0*qPos*qPos - 12.0*qPos + 1.0)*it->weight();
121 out[14] += (y[0]*n2[0] + y[1]*n2[1])*(1.0-20.0*qPos+90.0*pow(qPos,2)-140.0*pow(qPos,3)+70.0*pow(qPos,4))*it->weight()*sign2;
122
123 localPos[0] = qPos;
124 localPos[1] = 1.0;
125 y = f(localPos);
126 out[15] += (y[0]*n3[0] + y[1]*n3[1])*it->weight()*sign3;
127 out[16] += (y[0]*n3[0] + y[1]*n3[1])*(2.0*qPos - 1.0)*it->weight();
128 out[17] += (y[0]*n3[0] + y[1]*n3[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign3;
129 out[18] += (y[0]*n3[0] + y[1]*n3[1])*(20.0*qPos*qPos*qPos - 30.0*qPos*qPos + 12.0*qPos - 1.0)*it->weight();
130 out[19] += (y[0]*n3[0] + y[1]*n3[1])*(1.0-20.0*qPos+90.0*pow(qPos,2)-140.0*pow(qPos,3)+70.0*pow(qPos,4))*it->weight()*sign3;
131 }
132
134
135 for (typename QuadratureRule<Vector,2>::const_iterator it = rule2.begin();
136 it != rule2.end(); ++it)
137 {
138 FieldVector<double,2> qPos = it->position();
139
140 auto y = f(qPos);
141 std::vector<std::vector<double> > l(2,std::vector<double> (5));
142 l[0][0]=1.0;
143 l[1][0]=1.0;
144 l[0][1]=2.0*qPos[0]-1.0;
145 l[1][1]=2.0*qPos[1]-1.0;
146 l[0][2]=6.0*qPos[0]*qPos[0]-6.0*qPos[0]+1.0;
147 l[1][2]=6.0*qPos[1]*qPos[1]-6.0*qPos[1]+1.0;
148 l[0][3]=20.0*qPos[0]*qPos[0]*qPos[0] - 30.0*qPos[0]*qPos[0] + 12.0*qPos[0] - 1.0;
149 l[1][3]=20.0*qPos[1]*qPos[1]*qPos[1] - 30.0*qPos[1]*qPos[1] + 12.0*qPos[1] - 1.0;
150 l[0][4]=1.0-20.0*qPos[0]+90.0*pow(qPos[0],2)-140.0*pow(qPos[0],3)+70.0*pow(qPos[0],4);
151 l[1][4]=1.0-20.0*qPos[1]+90.0*pow(qPos[1],2)-140.0*pow(qPos[1],3)+70.0*pow(qPos[1],4);
152
153 for (int i=0;i<4;i++)
154 for (int j=0;j<5;j++)
155 out[20+i*5+j] +=y[0]*l[0][i]*l[1][j]*it->weight();
156
157 for (int i=0;i<5;i++)
158 for (int j=0;j<4;j++)
159 out[40+i*4+j] +=y[1]*l[0][i]*l[1][j]*it->weight();
160 }
161 }
162
163 private:
164 typename LB::Traits::RangeFieldType sign0, sign1, sign2, sign3;
165 typename LB::Traits::DomainType n0, n1, n2, n3;
166 };
167}
168
169#endif // DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS3_CUBE2D_LOCALINTERPOLATION_HH
vector space out of a tensor product of fields.
Definition: fvector.hh:96
Abstract base class for quadrature rules.
Definition: quadraturerules.hh:126
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:254
Second order Raviart-Thomas shape functions on the reference triangle.
Definition: raviartthomas4cube2dlocalinterpolation.hh:24
RT4Cube2DLocalInterpolation()
Standard constructor.
Definition: raviartthomas4cube2dlocalinterpolation.hh:28
RT4Cube2DLocalInterpolation(unsigned int s)
Make set number s, where 0 <= s < 8.
Definition: raviartthomas4cube2dlocalinterpolation.hh:38
void interpolate(const F &ff, std::vector< C > &out) const
Interpolate a given function with shape functions.
Definition: raviartthomas4cube2dlocalinterpolation.hh:77
constexpr GeometryType cube(unsigned int dim)
Returns a GeometryType representing a hypercube of dimension dim.
Definition: type.hh:775
typename Overloads::ScalarType< std::decay_t< V > >::type Scalar
Element type of some SIMD type.
Definition: interface.hh:233
Dune namespace.
Definition: alignedallocator.hh:14
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