/usr/include/dune/localfunctions/lagrange/q2/q2localbasis.hh is in libdune-localfunctions-dev 2.2.1-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 | // -*- tab-width: 2; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=2 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
|