/usr/include/dune/localfunctions/lagrange/q2/q2localbasis.hh is in libdune-localfunctions-dev 2.3.1-1.
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_Q2_LOCALBASIS_HH
#define DUNE_Q2_LOCALBASIS_HH
#include <dune/common/fmatrix.hh>
#include <dune/localfunctions/common/localbasis.hh>
namespace Dune
{
/**@ingroup LocalBasisImplementation
\brief Lagrange shape functions of order 2 on the reference cube
Also known as \f$Q^2\f$.
\tparam D Type to represent the field in the domain.
\tparam R Type to represent the field in the range.
\tparam dim Dimension of the reference cube
\nosubgrouping
*/
template<class D, class R, int dim>
class Q2LocalBasis
{
public:
typedef LocalBasisTraits<D,dim,Dune::FieldVector<D,dim>,R,1,Dune::FieldVector<R,1>,
Dune::FieldMatrix<R,1,dim> > Traits;
//! \brief number of shape functions
unsigned int size () const
{
int size = 1;
for (int i=0; i<dim; i++)
size *= 3;
return size;
}
//! \brief Evaluate all shape functions
inline void evaluateFunction (const typename Traits::DomainType& in,
std::vector<typename Traits::RangeType>& out) const
{
out.resize(size());
// Evaluate the Lagrange functions
array<array<R,3>, dim> X;
for (size_t i=0; i<dim; i++) {
X[i][0] = R(2)*in[i]*in[i] - R(3)*in[i]+R(1);
X[i][1] = -R(4)*in[i]*in[i] + R(4)*in[i];
X[i][2] = R(2)*in[i]*in[i] - in[i];
}
// Compute function values: they are products of 1d Lagrange function values
for (size_t i=0; i<out.size(); i++) {
out[i] = 1;
// Construct the i-th Lagrange point
size_t ternary = i;
for (int j=0; j<dim; j++) {
int digit = ternary%3;
ternary /= 3;
// Multiply the 1d Lagrange shape functions together
out[i] *= X[j][digit];
}
}
}
//! \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(size());
// Evaluate the 1d Lagrange functions and their derivatives
array<array<R,3>, dim> X, DX;
for (size_t i=0; i<dim; i++) {
X[i][0] = R(2)*in[i]*in[i] - R(3)*in[i]+R(1);
X[i][1] = -R(4)*in[i]*in[i] + R(4)*in[i];
X[i][2] = R(2)*in[i]*in[i] - in[i];
DX[i][0] = R(4)*in[i] - R(3);
DX[i][1] = -R(8)*in[i] + R(4);
DX[i][2] = R(4)*in[i] - R(1);
}
// Compute the derivatives by deriving the products of 1d Lagrange functions
for (size_t i=0; i<out.size(); i++) {
// Computing the j-th partial derivative
for (int j=0; j<dim; j++) {
out[i][0][j] = 1;
// Loop over the 'dim' terms in the product rule
size_t ternary = i;
for (int k=0; k<dim; k++) {
int digit = ternary%3;
ternary /= 3;
out[i][0][j] *= (k==j) ? DX[k][digit] : X[k][digit];
}
}
}
}
//! \brief Polynomial order of the shape functions
unsigned int order () const
{
return 2;
}
};
}
#endif
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