Reference documentation for deal.II version 8.1.0
Public Member Functions | Static Public Attributes | Protected Member Functions | Protected Attributes | List of all members
TensorProductPolynomials< dim, POLY > Class Template Reference

#include <tensor_product_polynomials.h>

Inheritance diagram for TensorProductPolynomials< dim, POLY >:
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Public Member Functions

template<class Pol >
 TensorProductPolynomials (const std::vector< Pol > &pols)
 
void output_indices (std::ostream &out) const
 
void set_numbering (const std::vector< unsigned int > &renumber)
 
const std::vector< unsigned int > & get_numbering () const
 
const std::vector< unsigned int > & get_numbering_inverse () const
 
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
 

Static Public Attributes

static const unsigned int dimension = dim
 

Protected Member Functions

void compute_index (const unsigned int i, unsigned int(&indices)[(dim >0?dim:1)]) const
 

Protected Attributes

std::vector< POLY > polynomials
 
unsigned int n_tensor_pols
 
std::vector< unsigned intindex_map
 
std::vector< unsigned intindex_map_inverse
 

Detailed Description

template<int dim, typename POLY = Polynomials::Polynomial<double>>
class TensorProductPolynomials< dim, POLY >

Tensor product of given polynomials.

Given a vector of n one-dimensional polynomials P1 to Pn, this class generates ndim polynomials of the form Qijk(x,y,z) = Pi(x)Pj(y)Pk(z). If the base polynomials are mutually orthogonal on the interval [-1,1] or [0,1], then the tensor product polynomials are orthogonal on [-1,1]dim or [0,1]dim, 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 P1(x)P1(y), P2(x)P1(y), P3(x)P1(y), ..., P1(x)P2(y), P2(x)P2(y), P3(x)P2(y), ... and likewise in 3d.

The output_indices() function prints the ordering of the dim-dimensional polynomials, i.e. for each polynomial in the polynomial space it gives the indices i,j,k of the one-dimensional polynomials in x,y and z direction. The ordering of the dim-dimensional polynomials can be changed by using the set_numbering() function.

Author
Ralf Hartmann, 2000, 2004, Guido Kanschat, 2000, Wolfgang Bangerth 2003

Definition at line 28 of file mapping_q.h.

Constructor & Destructor Documentation

template<int dim, typename POLY = Polynomials::Polynomial<double>>
template<class Pol >
TensorProductPolynomials< dim, POLY >::TensorProductPolynomials ( const std::vector< Pol > &  pols)

Constructor. pols is a vector of objects that should be derived or otherwise convertible to one-dimensional polynomial objects of type POLY (template argument of class). It will be copied element by element into a private variable.

Member Function Documentation

template<int dim, typename POLY = Polynomials::Polynomial<double>>
void TensorProductPolynomials< dim, POLY >::output_indices ( std::ostream &  out) const

Prints the list of the indices to out.

template<int dim, typename POLY = Polynomials::Polynomial<double>>
void TensorProductPolynomials< dim, POLY >::set_numbering ( const std::vector< unsigned int > &  renumber)

Sets the ordering of the polynomials. Requires renumber.size()==n(). Stores a copy of renumber.

template<int dim, typename POLY = Polynomials::Polynomial<double>>
const std::vector<unsigned int>& TensorProductPolynomials< dim, POLY >::get_numbering ( ) const

Gives read access to the renumber vector.

template<int dim, typename POLY = Polynomials::Polynomial<double>>
const std::vector<unsigned int>& TensorProductPolynomials< dim, POLY >::get_numbering_inverse ( ) const

Gives read access to the inverse renumber vector.

template<int dim, typename POLY = Polynomials::Polynomial<double>>
void TensorProductPolynomials< dim, POLY >::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(). 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, typename POLY = Polynomials::Polynomial<double>>
double TensorProductPolynomials< dim, POLY >::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 with values.size()==n() to get the point values of all tensor polynomials all at once and in a much more efficient way.

template<int dim, typename POLY = Polynomials::Polynomial<double>>
Tensor<1,dim> TensorProductPolynomials< dim, POLY >::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() to get the point value of all tensor polynomials all at once and in a much more efficient way.

template<int dim, typename POLY = Polynomials::Polynomial<double>>
Tensor<2,dim> TensorProductPolynomials< dim, POLY >::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() to get the point value of all tensor polynomials all at once and in a much more efficient way.

template<int dim, typename POLY = Polynomials::Polynomial<double>>
unsigned int TensorProductPolynomials< dim, POLY >::n ( ) const

Returns the number of tensor product polynomials. For n 1d polynomials this is ndim.

template<int dim, typename POLY = Polynomials::Polynomial<double>>
void TensorProductPolynomials< dim, POLY >::compute_index ( const unsigned int  i,
unsigned int(&)  indices[(dim >0?dim:1)] 
) const
protected

Each tensor product polynomial 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.

Member Data Documentation

template<int dim, typename POLY = Polynomials::Polynomial<double>>
const unsigned int TensorProductPolynomials< dim, POLY >::dimension = dim
static

Access to the dimension of this object, for checking and automatic setting of dimension in other classes.

Definition at line 74 of file tensor_product_polynomials.h.

template<int dim, typename POLY = Polynomials::Polynomial<double>>
std::vector<POLY> TensorProductPolynomials< dim, POLY >::polynomials
protected

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

Definition at line 179 of file tensor_product_polynomials.h.

template<int dim, typename POLY = Polynomials::Polynomial<double>>
unsigned int TensorProductPolynomials< dim, POLY >::n_tensor_pols
protected

Number of tensor product polynomials. See n().

Definition at line 184 of file tensor_product_polynomials.h.

template<int dim, typename POLY = Polynomials::Polynomial<double>>
std::vector<unsigned int> TensorProductPolynomials< dim, POLY >::index_map
protected

Index map for reordering the polynomials.

Definition at line 189 of file tensor_product_polynomials.h.

template<int dim, typename POLY = Polynomials::Polynomial<double>>
std::vector<unsigned int> TensorProductPolynomials< dim, POLY >::index_map_inverse
protected

Index map for reordering the polynomials.

Definition at line 194 of file tensor_product_polynomials.h.


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