/usr/include/dune/localfunctions/hierarchical/hierarchicalprismp2/hierarchicalprismp2localbasis.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_HIERARCHICAL_PRISM_P2_LOCALBASIS_HH
#define DUNE_HIERARCHICAL_PRISM_P2_LOCALBASIS_HH
/** \file
\brief Hierarchical prism p2 shape functions for the simplex
*/
#include <numeric>
#include <dune/common/fvector.hh>
#include <dune/common/fmatrix.hh>
#include <dune/localfunctions/common/localbasis.hh>
namespace Dune
{
template<class D, class R>
class HierarchicalPrismP2LocalBasis
{
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 18;
}
//! \brief Evaluate all shape functions
void evaluateFunction (const typename Traits::DomainType& in,
std::vector<typename Traits::RangeType> & out) const
{
out.resize(18);
out[0]=(1.0-in[0]-in[1])*(1.0-in[2]);
out[1]= in[0]*(1-in[2]);
out[2]=in[1]*(1-in[2]);
out[3]=in[2]*(1.0-in[0]-in[1]);
out[4]=in[0]*in[2];
out[5]=in[1]*in[2];
//edges
out[6]=2*(1.0-in[0]-in[1])*(0.5-in[0]-in[1])*(4*in[2]-4*in[2]*in[2]);
out[7]=2*in[0]*(-0.5+in[0])*(4*in[2]-4*in[2]*in[2]);
out[8]=2*in[1]*(-0.5+in[1])*(4*in[2]-4*in[2]*in[2]);
out[9]=4*in[0]*(1-in[0]-in[1])*(1-3*in[2]+2*in[2]*in[2]);
out[10]=4*in[1]*(1-in[0]-in[1])*(1-3*in[2]+2*in[2]*in[2]);
out[11]=4*in[0]*in[1]*(1-3*in[2]+2*in[2]*in[2]);
out[12]=4*in[0]*(1-in[0]-in[1])*(-in[2]+2*in[2]*in[2]);
out[13]=4*in[1]*(1-in[0]-in[1])*(-in[2]+2*in[2]*in[2]);
out[14]=4*in[0]*in[1]*(-in[2]+2*in[2]*in[2]);
//faces
out[15]=4*in[0]*(1-in[0]-in[1])*(4*in[2]-4*in[2]*in[2]);
out[16]=4*in[1]*(1-in[0]-in[1])*(4*in[2]-4*in[2]*in[2]);
out[17]=4*in[0]*in[1]*(4*in[2]-4*in[2]*in[2]);
}
//! \brief Evaluate Jacobian of all shape functions
void evaluateJacobian (const typename Traits::DomainType& in, //position
std::vector<typename Traits::JacobianType>& out) const //return value
{
out.resize(18);
//vertices
out[0][0][0] = in[2]-1;
out[0][0][1] = in[2]-1;
out[0][0][2] = in[0]+in[1]-1;
out[1][0][0] = 1-in[2];
out[1][0][1] = 0;
out[1][0][2] =-in[0];
out[2][0][0] = 0;
out[2][0][1] = 1-in[2];
out[2][0][2] = -in[1];
out[3][0][0] = -in[2];
out[3][0][1] = -in[2];
out[3][0][2] = 1-in[0]-in[1];
out[4][0][0] = in[2];
out[4][0][1] = 0;
out[4][0][2] = in[0];
out[5][0][0] = 0;
out[5][0][1] = in[2];
out[5][0][2] = in[1];
//edges
out[6][0][0] = (-3+4*in[0]+4*in[1])*(4*in[2]-4*in[2]*in[2]);
out[6][0][1] = (-3+4*in[0]+4*in[1])*(4*in[2]-4*in[2]*in[2]);
out[6][0][2] = 2*(1-in[0]-in[1])*(0.5-in[0]-in[1])*(4-8*in[2]);
out[7][0][0] = (-1+4*in[0])*(4*in[2]-4*in[2]*in[2]);
out[7][0][1] = 0;
out[7][0][2] = 2*in[0]*(-0.5+in[0])*(4-8*in[2]);
out[8][0][0] = 0;
out[8][0][1] = (-1+4*in[1])*(4*in[2]-4*in[2]*in[2]);
out[8][0][2] = 2*in[1]*(-0.5+in[1])*(4-8*in[2]);
out[9][0][0] = (4-8*in[0]-4*in[1])*(1-3*in[2]+2*in[2]*in[2]);
out[9][0][1] = -4*in[0]*(1-3*in[2]+2*in[2]*in[2]);
out[9][0][2] = 4*in[0]*(1-in[0]-in[1])*(-3+4*in[2]);
out[10][0][0] = (-4*in[1])*(1-3*in[2]+2*in[2]*in[2]);
out[10][0][1] = (4-4*in[0]-8*in[1])*(1-3*in[2]+2*in[2]*in[2]);
out[10][0][2] = 4*in[1]*(1-in[0]-in[1])*(-3+4*in[2]);
out[11][0][0] = 4*in[1]*(1-3*in[2]+2*in[2]*in[2]);
out[11][0][1] = 4*in[0]*(1-3*in[2]+2*in[2]*in[2]);
out[11][0][2] = 4*in[0]*in[1]*(-3+4*in[2]);
out[12][0][0] = (4-8*in[0]-4*in[1])*(-in[2]+2*in[2]*in[2]);
out[12][0][1] = (-4*in[0])*(-in[2]+2*in[2]*in[2]);
out[12][0][2] = 4*in[0]*(1-in[0]-in[1])*(-1+4*in[2]);
out[13][0][0] = -4*in[1]*(-in[2]+2*in[2]*in[2]);
out[13][0][1] = (4-4*in[0]-8*in[1])*(-in[2]+2*in[2]*in[2]);
out[13][0][2] = 4*in[1]*(1-in[0]-in[1])*(-1+4*in[2]);
out[14][0][0] = 4*in[1]*(-in[2]+2*in[2]*in[2]);
out[14][0][1] = 4*in[0]*(-in[2]+2*in[2]*in[2]);
out[14][0][2] = 4*in[0]*in[1]*(-1+4*in[2]);
//faces
out[15][0][0] = (4-8*in[0]-4*in[1])*(4*in[2]-4*in[2]*in[2]);
out[15][0][1] = -4*in[0]*(4*in[2]-4*in[2]*in[2]);
out[15][0][2] = 4*in[0]*(1-in[0]-in[1])*(4-8*in[2]);
out[16][0][0] = -4*in[1]*(4*in[2]-4*in[2]*in[2]);
out[16][0][1] = (4-4*in[0]-8*in[1])*(4*in[2]-4*in[2]*in[2]);
out[16][0][2] = 4*in[1]*(1-in[0]-in[1])*(4-8*in[2]);
out[17][0][0] = 4*in[1]*(4*in[2]-4*in[2]*in[2]);
out[17][0][1] = 4*in[0]*(4*in[2]-4*in[2]*in[2]);
out[17][0][2] = 4*in[0]*in[1]*(4-8*in[2]);
}
//! \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));
switch (direction) {
case 0:
out[0] = in[2]-1;
out[1] = 1-in[2];
out[2] = 0;
out[3] = -in[2];
out[4] = in[2];
out[5] = 0;
out[6] = (-3+4*in[0]+4*in[1])*(4*in[2]-4*in[2]*in[2]);
out[7] = (-1+4*in[0])*(4*in[2]-4*in[2]*in[2]);
out[8] = 0;
out[9] = (4-8*in[0]-4*in[1])*(1-3*in[2]+2*in[2]*in[2]);
out[10] = (-4*in[1])*(1-3*in[2]+2*in[2]*in[2]);
out[11] = 4*in[1]*(1-3*in[2]+2*in[2]*in[2]);
out[12] = (4-8*in[0]-4*in[1])*(-in[2]+2*in[2]*in[2]);
out[13] = -4*in[1]*(-in[2]+2*in[2]*in[2]);
out[14] = 4*in[1]*(-in[2]+2*in[2]*in[2]);
out[15] = (4-8*in[0]-4*in[1])*(4*in[2]-4*in[2]*in[2]);
out[16] = -4*in[1]*(4*in[2]-4*in[2]*in[2]);
out[17] = 4*in[1]*(4*in[2]-4*in[2]*in[2]);
break;
case 1:
out[0] = in[2]-1;
out[1] = 0;
out[2] = 1-in[2];
out[3] = -in[2];
out[4] = 0;
out[5] = in[2];
out[6] = (-3+4*in[0]+4*in[1])*(4*in[2]-4*in[2]*in[2]);
out[7] = 0;
out[8] = (-1+4*in[1])*(4*in[2]-4*in[2]*in[2]);
out[9] = -4*in[0]*(1-3*in[2]+2*in[2]*in[2]);
out[10] = (4-4*in[0]-8*in[1])*(1-3*in[2]+2*in[2]*in[2]);
out[11] = 4*in[0]*(1-3*in[2]+2*in[2]*in[2]);
out[12] = (-4*in[0])*(-in[2]+2*in[2]*in[2]);
out[13] = (4-4*in[0]-8*in[1])*(-in[2]+2*in[2]*in[2]);
out[14] = 4*in[0]*(-in[2]+2*in[2]*in[2]);
out[15] = -4*in[0]*(4*in[2]-4*in[2]*in[2]);
out[16] = (4-4*in[0]-8*in[1])*(4*in[2]-4*in[2]*in[2]);
out[17] = 4*in[0]*(4*in[2]-4*in[2]*in[2]);
break;
case 2:
out[0] = in[0]+in[1]-1;
out[1] =-in[0];
out[2] = -in[1];
out[3] = 1-in[0]-in[1];
out[4] = in[0];
out[5] = in[1];
out[6] = 2*(1-in[0]-in[1])*(0.5-in[0]-in[1])*(4-8*in[2]);
out[7] = 2*in[0]*(-0.5+in[0])*(4-8*in[2]);
out[8] = 2*in[1]*(-0.5+in[1])*(4-8*in[2]);
out[9] = 4*in[0]*(1-in[0]-in[1])*(-3+4*in[2]);
out[10] = 4*in[1]*(1-in[0]-in[1])*(-3+4*in[2]);
out[11] = 4*in[0]*in[1]*(-3+4*in[2]);
out[12] = 4*in[0]*(1-in[0]-in[1])*(-1+4*in[2]);
out[13] = 4*in[1]*(1-in[0]-in[1])*(-1+4*in[2]);
out[14] = 4*in[0]*in[1]*(-1+4*in[2]);
out[15] = 4*in[0]*(1-in[0]-in[1])*(4-8*in[2]);
out[16] = 4*in[1]*(1-in[0]-in[1])*(4-8*in[2]);
out[17] = 4*in[0]*in[1]*(4-8*in[2]);
break;
default:
DUNE_THROW(RangeError, "Component out of range.");
}
} else {
DUNE_THROW(NotImplemented, "Desired derivative order is not implemented");
}
}
/** \brief Polynomial order of the shape functions
*/
unsigned int order() const
{
return 2;
}
};
}
#endif
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