/usr/include/dune/localfunctions/rannacherturek/rannacherturek3d/rannacherturek3dlocalbasis.hh is in libdune-localfunctions-dev 2.5.0-2.
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_RANNACHER_TUREK_3D_LOCALBASIS_HH
#define DUNE_RANNACHER_TUREK_3D_LOCALBASIS_HH
#include <numeric>
#include <vector>
#include <dune/common/fvector.hh>
#include <dune/common/fmatrix.hh>
#include <dune/localfunctions/common/localbasis.hh>
namespace Dune
{
template< class D, class R >
class RannacherTurek3DLocalBasis
{
static const int coefficients[ 6 ][ 6 ];
public:
typedef LocalBasisTraits< D, 3, FieldVector< D, 3 >,
R, 1, FieldVector< R, 1 >,
FieldMatrix< R, 1, 3 > > Traits;
//! \brief number of shape functions
unsigned int size () const
{
return 6;
}
//! \brief evaluate all shape functions
inline void evaluateFunction ( const typename Traits::DomainType &in,
std::vector< typename Traits::RangeType > &out ) const
{
typedef typename Traits::RangeFieldType RangeFieldType;
RangeFieldType y[ 6 ] = { 1, in[ 0 ], in[ 1 ], in[ 2 ],
in[ 0 ]*in[ 0 ] - in[ 1 ]*in[ 1 ],
in[ 1 ]*in[ 1 ] - in[ 2 ]*in[ 2 ] };
out.resize( size() );
for( unsigned int i = 0; i < size(); ++i )
{
out[ i ] = RangeFieldType( 0 );
for( unsigned int j = 0; j < 6; ++j )
out[ i ] += coefficients[ i ][ j ]*y[ j ];
out[ i ] /= RangeFieldType( 3 );
}
}
//! \brief evaluate jacobian of all shape functions
inline void evaluateJacobian ( const typename Traits::DomainType &in,
std::vector< typename Traits::JacobianType > &out ) const
{
typedef typename Traits::RangeFieldType RangeFieldType;
RangeFieldType y0[ 5 ] = { 1, 0, 0, 2*in[ 0 ], 0 };
RangeFieldType y1[ 5 ] = { 0, 1, 0, -2*in[ 1 ], 2*in[ 1 ] };
RangeFieldType y2[ 5 ] = { 0, 0, 1, 0, -2*in[ 2 ] };
out.resize( size() );
for( unsigned int i = 0; i < size(); ++i )
{
out[ i ] = RangeFieldType( 0 );
for( unsigned int j = 0; j < 5; ++j )
{
out[ i ][ 0 ][ 0 ] += coefficients[ i ][ j+1 ]*y0[ j ];
out[ i ][ 0 ][ 1 ] += coefficients[ i ][ j+1 ]*y1[ j ];
out[ i ][ 0 ][ 2 ] += coefficients[ i ][ j+1 ]*y2[ j ];
}
out[ i ] /= RangeFieldType( 3 );
}
}
//! \brief Evaluate partial derivatives of all shape functions
void partial (const std::array<unsigned int, 3>& order,
const typename Traits::DomainType& in, // position
std::vector<typename Traits::RangeType>& out) const // return value
{
auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
if (totalOrder == 0) {
evaluateFunction(in, out);
} else if (totalOrder == 1) {
out.resize(size());
auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
using RangeFieldType = typename Traits::RangeFieldType;
RangeFieldType y[3][5] = { { 1.0, 0.0, 0.0, 2*in[0], 0.0 },
{ 0.0, 1.0, 0.0, -2*in[1], 2*in[1] },
{ 0.0, 0.0, 1.0, 0.0, -2*in[2] } };
for (std::size_t i = 0; i < size(); ++i) {
out[i] = RangeFieldType{0};
for (std::size_t j = 0; j < 5; ++j)
out[i] += coefficients[i][j+1] * y[direction][j];
out[i] /= RangeFieldType{3};
}
} else {
DUNE_THROW(NotImplemented, "Desired derivative order is not implemented");
}
}
//! \brief polynomial order of the shape functions
unsigned int order () const
{
return 2;
}
};
// RannacherTurek3DLocalBasis::coefficients
// ----------------------------------------
template< class D, class R >
const int RannacherTurek3DLocalBasis< D, R >
::coefficients[ 6 ][ 6 ] = {{ 2, -7, 2, 2, 4, 2 },
{ -1, -1, 2, 2, 4, 2 },
{ 2, 2, -7, 2, -2, 2 },
{ -1, 2, -1, 2, -2, 2 },
{ 2, 2, 2, -7, -2, -4 },
{ -1, 2, 2, -1, -2, -4 }};
} //namespace Dune
#endif // #ifndef DUNE_RANNACHER_TUREK_3D_LOCALBASIS_HH
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