/usr/include/dune/localfunctions/raviartthomas/raviartthomas3cube2d/raviartthomas3cube2dlocalinterpolation.hh is in libdune-localfunctions-dev 2.5.0-2.
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#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
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