TensorProductPolynomials< dim, PolynomialType > Class Template Reference

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

Inheritance diagram for TensorProductPolynomials< dim, PolynomialType >:

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, 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

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< PolynomialType >	polynomials
unsigned int	n_tensor_pols
std::vector< unsigned int >	index_map
std::vector< unsigned int >	index_map_inverse

Detailed Description

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

Tensor product of given polynomials.

Given a vector of n one-dimensional polynomials P₁ to P_n, this class generates n^dim polynomials of the form Q_ijk(x,y,z) = P_i(x)P_j(y)P_k(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 65 of file tensor_product_polynomials.h.

Constructor & Destructor Documentation

template<int dim, typename PolynomialType = Polynomials::Polynomial<double>>

template<class Pol >

TensorProductPolynomials< dim, PolynomialType >::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 PolynomialType (template argument of class). It will be copied element by element into a private variable.

Member Function Documentation

template<int dim, typename PolynomialType >

void TensorProductPolynomials< dim, PolynomialType >::output_indices

(

std::ostream &

out

)

const

Print the list of the indices to out.

Definition at line 98 of file tensor_product_polynomials.cc.

template<int dim, typename PolynomialType >

void TensorProductPolynomials< dim, PolynomialType >::set_numbering

(

const std::vector< unsigned int > &

renumber

)

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

Definition at line 116 of file tensor_product_polynomials.cc.

template<int dim, typename PolynomialType = Polynomials::Polynomial<double>>

const std::vector<unsigned int>& TensorProductPolynomials< dim, PolynomialType >::get_numbering

(

)

const

Give read access to the renumber vector.

template<int dim, typename PolynomialType = Polynomials::Polynomial<double>>

const std::vector<unsigned int>& TensorProductPolynomials< dim, PolynomialType >::get_numbering_inverse

(

)

const

Give read access to the inverse renumber vector.

template<int dim, typename PolynomialType >

void TensorProductPolynomials< dim, PolynomialType >::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(). 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 245 of file tensor_product_polynomials.cc.

template<int dim, typename PolynomialType >

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

Definition at line 143 of file tensor_product_polynomials.cc.

template<int dim, typename PolynomialType = Polynomials::Polynomial<double>>

template<int order>

Tensor<order, dim> TensorProductPolynomials< dim, PolynomialType >::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.

template<int dim, typename PolynomialType >

Tensor< 1, dim > TensorProductPolynomials< dim, PolynomialType >::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() to get the point value of all tensor polynomials all at once and in a much more efficient way.

Definition at line 163 of file tensor_product_polynomials.cc.

template<int dim, typename PolynomialType >

Tensor< 2, dim > TensorProductPolynomials< dim, PolynomialType >::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() to get the point value of all tensor polynomials all at once and in a much more efficient way.

Definition at line 200 of file tensor_product_polynomials.cc.

template<int dim, typename PolynomialType = Polynomials::Polynomial<double>>

unsigned int TensorProductPolynomials< dim, PolynomialType >::n

(

)

const

Return the number of tensor product polynomials. For n 1d polynomials this is n^dim.

template<int dim, typename PolynomialType >

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

inlineprotected

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.

Definition at line 82 of file tensor_product_polynomials.cc.

Member Data Documentation

template<int dim, typename PolynomialType = Polynomials::Polynomial<double>>

const unsigned int TensorProductPolynomials< dim, PolynomialType >::dimension = dim

static

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

Definition at line 72 of file tensor_product_polynomials.h.

template<int dim, typename PolynomialType = Polynomials::Polynomial<double>>

std::vector<PolynomialType> TensorProductPolynomials< dim, PolynomialType >::polynomials

protected

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

Definition at line 203 of file tensor_product_polynomials.h.

template<int dim, typename PolynomialType = Polynomials::Polynomial<double>>

unsigned int TensorProductPolynomials< dim, PolynomialType >::n_tensor_pols

protected

Number of tensor product polynomials. See n().

Definition at line 208 of file tensor_product_polynomials.h.

template<int dim, typename PolynomialType = Polynomials::Polynomial<double>>

std::vector<unsigned int> TensorProductPolynomials< dim, PolynomialType >::index_map

protected

Index map for reordering the polynomials.

Definition at line 213 of file tensor_product_polynomials.h.

template<int dim, typename PolynomialType = Polynomials::Polynomial<double>>

std::vector<unsigned int> TensorProductPolynomials< dim, PolynomialType >::index_map_inverse

protected

Index map for reordering the polynomials.

Definition at line 218 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
• /mnt/data/darndt/Sources/dealii-clang-6.0.0/source/base/tensor_product_polynomials.cc