/usr/include/dune/localfunctions/rannacherturek/rannacherturek2d/rannacherturek2dlocalbasis.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_2D_LOCALBASIS_HH
#define DUNE_RANNACHER_TUREK_2D_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 >
struct RannacherTurek2DLocalBasis
{
typedef LocalBasisTraits< D, 2, FieldVector< D, 2 >,
R, 1, FieldVector< R, 1 >,
FieldMatrix< R, 1, 2 > > Traits;
//! \brief number of shape functions
unsigned int size () const
{
return 4;
}
//! \brief evaluate all shape functions
inline void evaluateFunction ( const typename Traits::DomainType &in,
std::vector< typename Traits::RangeType > &out ) const
{
out.resize(4);
typename Traits::DomainFieldType qbase = in[0]*in[0]-in[1]*in[1];
out[0] = .75 - 2*in[0] + in[1] + qbase;
out[1] = -.25 + in[1] + qbase;
out[2] = .75 + in[0] - 2*in[1] - qbase;
out[3] = -.25 + in[0] - qbase;
}
//! \brief evaluate jacobian of all shape functions
inline void evaluateJacobian ( const typename Traits::DomainType &in,
std::vector< typename Traits::JacobianType > &out ) const
{
out.resize(4);
// see http://www.dune-project.org/doc/doxygen/html/classDune_1_1C1LocalBasisInterface.html#d6f8368f8aa43439cc7ef10419f6e2ea
// out[i][j][k] = d_k \phi^i_j , where \phi^i_j is the j'th component of the i'th shape function.
out[0][0][0] = -2 + 2*in[0]; out[0][0][1] = 1 - 2*in[1];
out[1][0][0] = 2*in[0]; out[1][0][1] = 1 - 2*in[1];
out[2][0][0] = 1 - 2*in[0]; out[2][0][1] = -2 + 2*in[1];
out[3][0][0] = 1 - 2*in[0]; out[3][0][1] = 2*in[1];
}
//! \brief Evaluate partial derivatives of all shape functions
void partial (const std::array<unsigned int, 2>& 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) {
auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
out.resize(size());
switch (direction) {
case 0:
out[0] = -2 + 2*in[0];
out[1] = 2*in[0];
out[2] = 1 - 2*in[0];
out[3] = 1 - 2*in[0];
break;
case 1:
out[0] = 1 - 2*in[1];
out[1] = 1 - 2*in[1];
out[2] = -2 + 2*in[1];
out[3] = 2*in[1];
break;
default:
DUNE_THROW(RangeError, "Component out of range.");
}
} else if (totalOrder == 2) {
auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 2));
out.resize(size());
switch (direction) {
case 0:
out[0] = out[1] = 2;
out[2] = out[3] =-2;
break;
case 1:
out[0] = out[1] =-2;
out[2] = out[3] = 2;
break;
default:
out[0] = out[1] = out[2] = out[3] = 0;
break;
}
} else {
out[0] = out[1] = out[2] = out[3] = 0;
}
}
//! \brief polynomial order of the shape functions
unsigned int order () const
{
// must be 2 here since it contains x^2 and x^2
return 2;
}
};
} //namespace Dune
#endif // #ifndef DUNE_RANNACHER_TUREK_2D_LOCALBASIS_HH
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