AnisotropicPolynomials< dim > Class Template Reference
[Polynomials and polynomial spaces]

List of all members.

Public Member Functions

 AnisotropicPolynomials (const std::vector< std::vector< Polynomials::Polynomial< double > > > &pols)
void compute (const Point< dim > &unit_point, std::vector< double > &values, std::vector< Tensor< 1, dim > > &grads, std::vector< Tensor< 2, dim > > &grad_grads) const
double compute_value (const unsigned int i, const Point< dim > &p) const
Tensor< 1, dim > compute_grad (const unsigned int i, const Point< dim > &p) const
Tensor< 2, dim > compute_grad_grad (const unsigned int i, const Point< dim > &p) const
unsigned int n () const

Private Member Functions

void compute_index (const unsigned int i, unsigned int(&indices)[dim]) const

Static Private Member Functions

static unsigned int get_n_tensor_pols (const std::vector< std::vector< Polynomials::Polynomial< double > > > &pols)

Private Attributes

std::vector< std::vector
< Polynomials::Polynomial
< double > > > 
polynomials
unsigned int n_tensor_pols


Detailed Description

template<int dim>
class AnisotropicPolynomials< dim >

Anisotropic tensor product of given polynomials.

Given one-dimensional polynomials Px1, Px2, ... in x-direction, Py1, Py2, ... in y-direction, and so on, this class generates polynomials of the form Qijk(x,y,z) = Pxi(x)Pyj(y)Pzk(z). If the base polynomials are mutually orthogonal on the interval $[-1,1]$ or $[0,d]$, then the tensor product polynomials are orthogonal on $[-1,1]^d$ or $[0,1]^d$, respectively.

Indexing is as follows: the order of dim-dimensional polynomials is x-coordinates running fastest, then y-coordinate, etc. The first few polynomials are thus Px1(x)Py1(y), Px2(x)Py1(y), Px3(x)Py1(y), ..., Px1(x)Py2(y), Px2(x)Py2(y), Px3(x)Py2(y), ..., and likewise in 3d.

Author:
Wolfgang Bangerth 2003

Constructor & Destructor Documentation

template<int dim>
AnisotropicPolynomials< dim >::AnisotropicPolynomials ( const std::vector< std::vector< Polynomials::Polynomial< double > > > &  pols  ) 

Constructor. pols is a table of one-dimensional polynomials. The number of rows in this table should be equal to the space dimension, with the elements of each row giving the polynomials that shall be used in this particular coordinate direction. These polynomials may vary between coordinates, as well as their number.


Member Function Documentation

template<int dim>
void AnisotropicPolynomials< dim >::compute ( const Point< dim > &  unit_point,
std::vector< double > &  values,
std::vector< Tensor< 1, dim > > &  grads,
std::vector< Tensor< 2, dim > > &  grad_grads 
) const

Computes the value and the first and second derivatives of each tensor product polynomial at unit_point.

The size of the vectors must either be equal 0 or equal n_tensor_pols. In the first case, the function will not compute these values.

If you need values or derivatives of all tensor product polynomials then use this function, rather than using any of the compute_value, compute_grad or compute_grad_grad functions, see below, in a loop over all tensor product polynomials.

template<int dim>
double AnisotropicPolynomials< dim >::compute_value ( const unsigned int  i,
const Point< dim > &  p 
) const

Computes the value of the ith tensor product polynomial at unit_point. Here i is given in tensor product numbering.

Note, that using this function within a loop over all tensor product polynomials is not efficient, because then each point value of the underlying (one-dimensional) polynomials is (unnecessarily) computed several times. Instead use the compute function, see above, with values.size()==n_tensor_pols to get the point values of all tensor polynomials all at once and in a much more efficient way.

template<int dim>
Tensor<1,dim> AnisotropicPolynomials< dim >::compute_grad ( const unsigned int  i,
const Point< dim > &  p 
) const

Computes the grad of the ith tensor product polynomial at unit_point. Here i is given in tensor product numbering.

Note, that using this function within a loop over all tensor product polynomials is not efficient, because then each derivative value of the underlying (one-dimensional) polynomials is (unnecessarily) computed several times. Instead use the compute function, see above, with grads.size()==n_tensor_pols to get the point value of all tensor polynomials all at once and in a much more efficient way.

template<int dim>
Tensor<2,dim> AnisotropicPolynomials< dim >::compute_grad_grad ( const unsigned int  i,
const Point< dim > &  p 
) const

Computes the second derivative (grad_grad) of the ith tensor product polynomial at unit_point. Here i is given in tensor product numbering.

Note, that using this function within a loop over all tensor product polynomials is not efficient, because then each derivative value of the underlying (one-dimensional) polynomials is (unnecessarily) computed several times. Instead use the compute function, see above, with grad_grads.size()==n_tensor_pols to get the point value of all tensor polynomials all at once and in a much more efficient way.

template<int dim>
unsigned int AnisotropicPolynomials< dim >::n (  )  const

Returns the number of tensor product polynomials. It is the product of the number of polynomials in each coordinate direction.

template<int dim>
void AnisotropicPolynomials< dim >::compute_index ( const unsigned int  i,
unsigned int(&)  indices[dim] 
) const [private]

Each tensor product polynomial @þ{i} is a product of one-dimensional polynomials in each space direction. Compute the indices of these one-dimensional polynomials for each space direction, given the index i.

template<int dim>
static unsigned int AnisotropicPolynomials< dim >::get_n_tensor_pols ( const std::vector< std::vector< Polynomials::Polynomial< double > > > &  pols  )  [static, private]

Given the input to the constructor, compute n_tensor_pols.


Member Data Documentation

template<int dim>
std::vector<std::vector<Polynomials::Polynomial<double> > > AnisotropicPolynomials< dim >::polynomials [private]

Copy of the vector pols of polynomials given to the constructor.

template<int dim>
unsigned int AnisotropicPolynomials< dim >::n_tensor_pols [private]

Number of tensor product polynomials. This is Nx*Ny*Nz, or with terms dropped if the number of space dimensions is less than 3.


The documentation for this class was generated from the following file:

deal.II documentation generated on Sat Aug 15 16:51:39 2009 by doxygen 1.5.9