/usr/include/dune/localfunctions/lagrange/pyramidp1/pyramidp1localbasis.hh is in libdune-localfunctions-dev 2.5.0-2.
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// vi: set et ts=4 sw=2 sts=2:
#ifndef DUNE_PYRAMID_P1_LOCALBASIS_HH
#define DUNE_PYRAMID_P1_LOCALBASIS_HH
#include <numeric>
#include <dune/common/fmatrix.hh>
#include <dune/localfunctions/common/localbasis.hh>
namespace Dune
{
/**@ingroup LocalBasisImplementation
\brief Linear Lagrange shape functions on the pyramid.
Defines the linear shape functions on pyramid.
\tparam D Type to represent the field in the domain.
\tparam R Type to represent the field in the range.
\nosubgrouping
*/
template<class D, class R>
class PyramidP1LocalBasis
{
public:
//! \brief export type traits for function signature
typedef LocalBasisTraits<D,3,Dune::FieldVector<D,3>,R,1,Dune::FieldVector<R,1>,
Dune::FieldMatrix<R,1,3> > Traits;
//! \brief number of shape functions
unsigned int size () const
{
return 5;
}
//! \brief Evaluate all shape functions
inline void evaluateFunction (const typename Traits::DomainType& in, // position
std::vector<typename Traits::RangeType>& out) const // return value
{
out.resize(5);
if(in[0] > in[1])
{
out[0] = (1-in[0])*(1-in[1])-in[2]*(1-in[1]);
out[1] = in[0]*(1-in[1])-in[2]*in[1];
out[2] = (1-in[0])*in[1]-in[2]*in[1];
out[3] = in[0]*in[1]+in[2]*in[1];
}
else
{
out[0] = (1-in[0])*(1-in[1])-in[2]*(1-in[0]);
out[1] = in[0]*(1-in[1])-in[2]*in[0];
out[2] = (1-in[0])*in[1]-in[2]*in[0];
out[3] = in[0]*in[1]+in[2]*in[0];
}
out[4] = in[2];
}
//! \brief Evaluate Jacobian of all shape functions
inline void
evaluateJacobian (const typename Traits::DomainType& in, // position
std::vector<typename Traits::JacobianType>& out) const // return value
{
out.resize(5);
if(in[0] > in[1])
{
out[0][0][0] = -1 + in[1]; out[0][0][1] = -1 + in[0] + in[2]; out[0][0][2] = -1 + in[1];
out[1][0][0] = 1 - in[1]; out[1][0][1] = -in[0] - in[2]; out[1][0][2] = -in[1];
out[2][0][0] = -in[1]; out[2][0][1] = 1 - in[0] - in[2]; out[2][0][2] = -in[1];
out[3][0][0] = in[1]; out[3][0][1] = in[0]+in[2]; out[3][0][2] = in[1];
}
else
{
out[0][0][0] = -1 + in[1] + in[2]; out[0][0][1] = -1 + in[0]; out[0][0][2] = -1 + in[0];
out[1][0][0] = 1 - in[1] - in[2]; out[1][0][1] = -in[0]; out[1][0][2] = -in[0];
out[2][0][0] = -in[1] - in[2]; out[2][0][1] = 1 - in[0]; out[2][0][2] = -in[0];
out[3][0][0] = in[1] + in[2]; out[3][0][1] = in[0]; out[3][0][2] = in[0];
}
out[4][0][0] = 0; out[4][0][1] = 0; out[4][0][2] = 1;
}
//! \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));
if (in[0] > in[1])
{
switch (direction) {
case 0:
out[0] = -1 + in[1];
out[1] = 1 - in[1];
out[2] = -in[1];
out[3] = in[1];
out[4] = 0;
break;
case 1:
out[0] = -1 + in[0] + in[2];
out[1] = -in[0] - in[2];
out[2] = 1 - in[0] - in[2];
out[3] = in[0]+in[2];
out[4] = 0;
break;
case 2:
out[0] = -1 + in[1];
out[1] = -in[1];
out[2] = -in[1];
out[3] = in[1];
out[4] = 1;
break;
default:
DUNE_THROW(RangeError, "Component out of range.");
}
}
else /* (in[0] <= in[1]) */
{
switch (direction) {
case 0:
out[0] = -1 + in[1] + in[2];
out[1] = 1 - in[1] - in[2];
out[2] = -in[1] - in[2];
out[3] = in[1] + in[2];
out[4] = 0;
break;
case 1:
out[0] = -1 + in[0];
out[1] = -in[0];
out[2] = 1 - in[0];
out[3] = in[0];
out[4] = 0;
break;
case 2:
out[0] = -1 + in[0];
out[1] = -in[0];
out[2] = -in[0];
out[3] = in[0];
out[4] = 1;
break;
default:
DUNE_THROW(RangeError, "Component out of range.");
}
}
} else if (totalOrder == 2) {
out.resize(size());
if ((order[0] == 1 && order[1] == 1) ||
(order[1] == 1 && order[2] == 1 && in[0] > in[1]) ||
(order[0] == 1 && order[2] == 1 && in[0] <=in[1])) {
out[0] = 1;
out[1] =-1;
out[2] =-1;
out[3] = 1;
out[4] = 0;
} else {
for (std::size_t i = 0; i < size(); ++i)
out[i] = 0;
}
} else {
out.resize(size());
for (std::size_t i = 0; i < size(); ++i)
out[i] = 0;
}
}
//! \brief Polynomial order of the shape functions
unsigned int order () const
{
return 1;
}
};
}
#endif
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