AnisotropicPolynomials< dim > Class Template Reference

#include <deal.II/base/tensor_product_polynomials.h>

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, std::vector< Tensor< 3, dim > > &third_derivatives, std::vector< Tensor< 4, dim > > &fourth_derivatives) const
double	compute_value (const unsigned int i, const Point< dim > &p) const
template<int order>
Tensor< order, dim >	compute_derivative (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
const std::vector< std::vector< Polynomials::Polynomial< double > > >	polynomials
const 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 Q_ijk(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

Definition at line 245 of file tensor_product_polynomials.h.

Constructor & Destructor Documentation

AnisotropicPolynomials()

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.

Definition at line 442 of file tensor_product_polynomials.cc.

Member Function Documentation

compute()

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,
		std::vector< Tensor< 3, dim > > &	third_derivatives,
		std::vector< Tensor< 4, dim > > &	fourth_derivatives
	)		const

Compute 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.

Definition at line 564 of file tensor_product_polynomials.cc.

compute_value()

template<int dim>

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

Compute 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.

Definition at line 482 of file tensor_product_polynomials.cc.

compute_derivative()

template<int dim>

template<int order>

Tensor<order,dim> AnisotropicPolynomials< dim >::compute_derivative	(	const unsigned int	i,
		const Point< dim > &	p
	)		const

Compute the orderth derivative 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 the size of the appropriate parameter set to n() to get the point value of all tensor polynomials all at once and in a much more efficient way.

Template Parameters

order

The derivative order.

compute_grad()

template<int dim>

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

Compute 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.

Definition at line 498 of file tensor_product_polynomials.cc.

compute_grad_grad()

template<int dim>

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

Compute 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.

Definition at line 526 of file tensor_product_polynomials.cc.

n()

template<int dim>

unsigned int AnisotropicPolynomials< dim >::n

(

)

const

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

Definition at line 702 of file tensor_product_polynomials.cc.

compute_index()

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.

Definition at line 460 of file tensor_product_polynomials.cc.

get_n_tensor_pols()

template<int dim>

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

staticprivate

Given the input to the constructor, compute n_tensor_pols.

Definition at line 711 of file tensor_product_polynomials.cc.

Member Data Documentation

polynomials

template<int dim>

const std::vector<std::vector<Polynomials::Polynomial<double> > > AnisotropicPolynomials< dim >::polynomials

private

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

Definition at line 350 of file tensor_product_polynomials.h.

n_tensor_pols

template<int dim>

const 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.

Definition at line 356 of file tensor_product_polynomials.h.

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

• deal.II/base/tensor_product_polynomials.h
• source/base/tensor_product_polynomials.cc