/usr/include/dune/localfunctions/lagrange/pk3d/pk3dlocalbasis.hh is in libdune-localfunctions-dev 2.4.1-1.
This file is owned by root:root, with mode 0o644.
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// vi: set et ts=4 sw=2 sts=2:
#ifndef DUNE_PK3DLOCALBASIS_HH
#define DUNE_PK3DLOCALBASIS_HH
#include <dune/common/fmatrix.hh>
#include <dune/localfunctions/common/localbasis.hh>
namespace Dune
{
/**@ingroup LocalBasisImplementation
\brief Lagrange shape functions of arbitrary order on the reference tetrahedron.
Lagrange shape functions of arbitrary order have the property that
\f$\hat\phi^i(x_j) = \delta_{i,j}\f$ for certain points \f$x_j\f$.
\tparam D Type to represent the field in the domain.
\tparam R Type to represent the field in the range.
\tparam k Polynomial order.
\nosubgrouping
*/
template<class D, class R, unsigned int k>
class Pk3DLocalBasis
{
public:
enum {N = (k+1)*(k+2)*(k+3)/6};
enum {O = k};
typedef LocalBasisTraits<D,3,Dune::FieldVector<D,3>,R,1,Dune::FieldVector<R,1>,
Dune::FieldMatrix<R,1,3> > Traits;
//! \brief Standard constructor
Pk3DLocalBasis () {}
//! \brief number of shape functions
unsigned int size () const
{
return N;
}
//! \brief Evaluate all shape functions
inline void evaluateFunction (const typename Traits::DomainType& x,
std::vector<typename Traits::RangeType>& out) const
{
out.resize(N);
typename Traits::DomainType kx = x;
kx *= k;
unsigned int n = 0;
unsigned int i[4];
R factor[4];
for (i[2] = 0; i[2] <= k; ++i[2])
{
factor[2] = 1.0;
for (unsigned int j = 0; j < i[2]; ++j)
factor[2] *= (kx[2]-j) / (i[2]-j);
for (i[1] = 0; i[1] <= k - i[2]; ++i[1])
{
factor[1] = 1.0;
for (unsigned int j = 0; j < i[1]; ++j)
factor[1] *= (kx[1]-j) / (i[1]-j);
for (i[0] = 0; i[0] <= k - i[1] - i[2]; ++i[0])
{
factor[0] = 1.0;
for (unsigned int j = 0; j < i[0]; ++j)
factor[0] *= (kx[0]-j) / (i[0]-j);
i[3] = k - i[0] - i[1] - i[2];
D kx3 = k - kx[0] - kx[1] - kx[2];
factor[3] = 1.0;
for (unsigned int j = 0; j < i[3]; ++j)
factor[3] *= (kx3-j) / (i[3]-j);
out[n++] = factor[0] * factor[1] * factor[2] * factor[3];
}
}
}
}
//! \brief Evaluate Jacobian of all shape functions
inline void
evaluateJacobian (const typename Traits::DomainType& x, // position
std::vector<typename Traits::JacobianType>& out) const // return value
{
out.resize(N);
typename Traits::DomainType kx = x;
kx *= k;
unsigned int n = 0;
unsigned int i[4];
R factor[4];
for (i[2] = 0; i[2] <= k; ++i[2])
{
factor[2] = 1.0;
for (unsigned int j = 0; j < i[2]; ++j)
factor[2] *= (kx[2]-j) / (i[2]-j);
for (i[1] = 0; i[1] <= k - i[2]; ++i[1])
{
factor[1] = 1.0;
for (unsigned int j = 0; j < i[1]; ++j)
factor[1] *= (kx[1]-j) / (i[1]-j);
for (i[0] = 0; i[0] <= k - i[1] - i[2]; ++i[0])
{
factor[0] = 1.0;
for (unsigned int j = 0; j < i[0]; ++j)
factor[0] *= (kx[0]-j) / (i[0]-j);
i[3] = k - i[0] - i[1] - i[2];
D kx3 = k - kx[0] - kx[1] - kx[2];
R sum3 = 0.0;
factor[3] = 1.0;
for (unsigned int j = 0; j < i[3]; ++j)
factor[3] /= i[3] - j;
R prod_all = factor[0] * factor[1] * factor[2] * factor[3];
for (unsigned int j = 0; j < i[3]; ++j)
{
R prod = prod_all;
for (unsigned int l = 0; l < i[3]; ++l)
if (j == l)
prod *= -R(k);
else
prod *= kx3 - l;
sum3 += prod;
}
for (unsigned int j = 0; j < i[3]; ++j)
factor[3] *= kx3 - j;
for (unsigned int m = 0; m < 3; ++m)
{
out[n][0][m] = sum3;
for (unsigned int j = 0; j < i[m]; ++j)
{
R prod = factor[3];
for (unsigned int p = 0; p < 3; ++p)
{
if (m == p)
for (unsigned int l = 0; l < i[p]; ++l)
if (j == l)
prod *= R(k) / (i[p]-l);
else
prod *= (kx[p]-l) / (i[p]-l);
else
prod *= factor[p];
}
out[n][0][m] += prod;
}
}
n++;
}
}
}
}
//! \brief Polynomial order of the shape functions
unsigned int order () const
{
return k;
}
};
//Specialization for k=0
template<class D, class R>
class Pk3DLocalBasis<D,R,0>
{
public:
typedef LocalBasisTraits<D,3,Dune::FieldVector<D,3>,R,1,Dune::FieldVector<R,1>,
Dune::FieldMatrix<R,1,3> > Traits;
/** \brief Export the number of degrees of freedom */
enum {N = 1};
/** \brief Export the element order */
enum {O = 0};
unsigned int size () const
{
return 1;
}
inline void evaluateFunction (const typename Traits::DomainType& in,
std::vector<typename Traits::RangeType>& out) const
{
out.resize(1);
out[0] = 1;
}
// evaluate derivative of a single component
inline void
evaluateJacobian (const typename Traits::DomainType& in, // position
std::vector<typename Traits::JacobianType>& out) const // return value
{
out.resize(1);
out[0][0][0] = 0;
out[0][0][1] = 0;
out[0][0][2] = 0;
}
// local interpolation of a function
template<typename E, typename F, typename C>
void interpolate (const E& e, const F& f, std::vector<C>& out) const
{
typename Traits::DomainType x;
typename Traits::RangeType y;
x[0] = 1.0/4.0;
x[1] = 1.0/4.0;
x[2] = 1.0/4.0;
f.eval_local(e,x,y);
out[0] = y;
}
unsigned int order () const
{
return 0;
}
};
}
#endif
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