/usr/include/dune/localfunctions/raviartthomas/raviartthomas3cube2d/raviartthomas3cube2dlocalinterpolation.hh is in libdune-localfunctions-dev 2.4.1-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 | // -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=4 sw=2 sts=2:
#ifndef DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS3_CUBE2D_LOCALINTERPOLATION_HH
#define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS3_CUBE2D_LOCALINTERPOLATION_HH
#include <vector>
#include <dune/geometry/quadraturerules.hh>
namespace Dune
{
/**
* \ingroup LocalInterpolationImplementation
* \brief Second order Raviart-Thomas shape functions on the reference quadrilateral.
*
* \tparam LB corresponding LocalBasis giving traits
*
* \nosubgrouping
*/
template<class LB>
class RT3Cube2DLocalInterpolation
{
public:
//! \brief Standard constructor
RT3Cube2DLocalInterpolation ()
{
sign0 = sign1 = sign2 = sign3 = 1.0;
}
/**
* \brief Make set number s, where 0 <= s < 8
*
* \param s Edge orientation indicator
*/
RT3Cube2DLocalInterpolation (unsigned int s)
{
sign0 = sign1 = sign2 = sign3 = 1.0;
if (s & 1)
{
sign0 *= -1.0;
}
if (s & 2)
{
sign1 *= -1.0;
}
if (s & 4)
{
sign2 *= -1.0;
}
if (s & 8)
{
sign3 *= -1.0;
}
n0[0] = -1.0;
n0[1] = 0.0;
n1[0] = 1.0;
n1[1] = 0.0;
n2[0] = 0.0;
n2[1] = -1.0;
n3[0] = 0.0;
n3[1] = 1.0;
}
/**
* \brief Interpolate a given function with shape functions
*
* \tparam F Function type for function which should be interpolated
* \tparam C Coefficient type
* \param f function which should be interpolated
* \param out return value, vector of coefficients
*/
template<typename F, typename C>
void interpolate (const F& f, std::vector<C>& out) const
{
// f gives v*outer normal at a point on the edge!
typedef typename LB::Traits::RangeFieldType Scalar;
typedef typename LB::Traits::DomainFieldType Vector;
typename F::Traits::RangeType y;
out.resize(40);
fill(out.begin(), out.end(), 0.0);
const int qOrder = 9;
const QuadratureRule<Scalar,1>& rule = QuadratureRules<Scalar,1>::rule(GeometryType(GeometryType::cube,1), qOrder);
for (typename QuadratureRule<Scalar,1>::const_iterator it=rule.begin(); it!=rule.end(); ++it)
{
Scalar qPos = it->position();
typename LB::Traits::DomainType localPos;
localPos[0] = 0.0;
localPos[1] = qPos;
f.evaluate(localPos, y);
out[0] += (y[0]*n0[0] + y[1]*n0[1])*it->weight()*sign0;
out[1] += (y[0]*n0[0] + y[1]*n0[1])*(2.0*qPos - 1.0)*it->weight();
out[2] += (y[0]*n0[0] + y[1]*n0[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign0;
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();
localPos[0] = 1.0;
localPos[1] = qPos;
f.evaluate(localPos, y);
out[4] += (y[0]*n1[0] + y[1]*n1[1])*it->weight()*sign1;
out[5] += (y[0]*n1[0] + y[1]*n1[1])*(1.0 - 2.0*qPos)*it->weight();
out[6] += (y[0]*n1[0] + y[1]*n1[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign1;
out[7] += (y[0]*n1[0] + y[1]*n1[1])*(-20.0*qPos*qPos*qPos + 30.0*qPos*qPos - 12.0*qPos + 1.0)*it->weight();
localPos[0] = qPos;
localPos[1] = 0.0;
f.evaluate(localPos, y);
out[8] += (y[0]*n2[0] + y[1]*n2[1])*it->weight()*sign2;
out[9] += (y[0]*n2[0] + y[1]*n2[1])*(1.0 - 2.0*qPos)*it->weight();
out[10] += (y[0]*n2[0] + y[1]*n2[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign2;
out[11] += (y[0]*n2[0] + y[1]*n2[1])*(-20.0*qPos*qPos*qPos + 30.0*qPos*qPos - 12.0*qPos + 1.0)*it->weight();
localPos[0] = qPos;
localPos[1] = 1.0;
f.evaluate(localPos, y);
out[12] += (y[0]*n3[0] + y[1]*n3[1])*it->weight()*sign3;
out[13] += (y[0]*n3[0] + y[1]*n3[1])*(2.0*qPos - 1.0)*it->weight();
out[14] += (y[0]*n3[0] + y[1]*n3[1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*it->weight()*sign3;
out[15] += (y[0]*n3[0] + y[1]*n3[1])*(20.0*qPos*qPos*qPos - 30.0*qPos*qPos + 12.0*qPos - 1.0)*it->weight();
}
const QuadratureRule<Vector,2>& rule2 = QuadratureRules<Vector,2>::rule(GeometryType(GeometryType::cube,2), qOrder);
for (typename QuadratureRule<Vector,2>::const_iterator it = rule2.begin();
it != rule2.end(); ++it)
{
FieldVector<double,2> qPos = it->position();
f.evaluate(qPos, y);
double l0_x=1.0;
double l1_x=2.0*qPos[0]-1.0;
double l2_x=6.0*qPos[0]*qPos[0]-6.0*qPos[0]+1.0;
double l3_x=20.0*qPos[0]*qPos[0]*qPos[0] - 30.0*qPos[0]*qPos[0] + 12.0*qPos[0] - 1.0;
double l0_y=1.0;
double l1_y=2.0*qPos[1]-1.0;
double l2_y=6.0*qPos[1]*qPos[1]-6.0*qPos[1]+1.0;
double l3_y=20.0*qPos[1]*qPos[1]*qPos[1] - 30.0*qPos[1]*qPos[1] + 12.0*qPos[1] - 1.0;
out[16] += y[0]*l0_x*l0_y*it->weight();
out[17] += y[0]*l0_x*l1_y*it->weight();
out[18] += y[0]*l0_x*l2_y*it->weight();
out[19] += y[0]*l0_x*l3_y*it->weight();
out[20] += y[0]*l1_x*l0_y*it->weight();
out[21] += y[0]*l1_x*l1_y*it->weight();
out[22] += y[0]*l1_x*l2_y*it->weight();
out[23] += y[0]*l1_x*l3_y*it->weight();
out[24] += y[0]*l2_x*l0_y*it->weight();
out[25] += y[0]*l2_x*l1_y*it->weight();
out[26] += y[0]*l2_x*l2_y*it->weight();
out[27] += y[0]*l2_x*l3_y*it->weight();
out[28] += y[1]*l0_x*l0_y*it->weight();
out[29] += y[1]*l0_x*l1_y*it->weight();
out[30] += y[1]*l0_x*l2_y*it->weight();
out[31] += y[1]*l1_x*l0_y*it->weight();
out[32] += y[1]*l1_x*l1_y*it->weight();
out[33] += y[1]*l1_x*l2_y*it->weight();
out[34] += y[1]*l2_x*l0_y*it->weight();
out[35] += y[1]*l2_x*l1_y*it->weight();
out[36] += y[1]*l2_x*l2_y*it->weight();
out[37] += y[1]*l3_x*l0_y*it->weight();
out[38] += y[1]*l3_x*l1_y*it->weight();
out[39] += y[1]*l3_x*l2_y*it->weight();
}
}
private:
typename LB::Traits::RangeFieldType sign0, sign1, sign2, sign3;
typename LB::Traits::DomainType n0, n1, n2, n3;
};
}
#endif // DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS3_CUBE2D_LOCALINTERPOLATION_HH
|