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

Public Member Functions
template<class Pol >
	TensorProductPolynomialsBubbles (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	evaluate (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 override

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

std::string	name () const override

virtual std::unique_ptr< ScalarPolynomialsBase< dim > >	clone () const override

double	compute_value (const unsigned int, const Point< 0 > &) const

Static Public Attributes
static const unsigned int	dimension = dim

Private Attributes
TensorProductPolynomials< dim >	tensor_polys

std::vector< unsigned int >	index_map

std::vector< unsigned int >	index_map_inverse

Detailed Description

template<int dim>
class TensorProductPolynomialsBubbles< dim >

Tensor product of given polynomials and bubble functions of form \((2*x_j-1)^{degree-1}\prod_{i=0}^{dim-1}(x_i(1-x_i))\). This class inherits most of its functionality from TensorProductPolynomials. The bubble enrichments are added for the last indices. index.

Author: Daniel Arndt, 2015

Definition at line 37 of file tensor_product_polynomials.h.

Constructor & Destructor Documentation

◆ TensorProductPolynomialsBubbles()

template<int dim>

template<class Pol >

TensorProductPolynomialsBubbles< dim >::TensorProductPolynomialsBubbles ( const std::vector< Pol > & pols )

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

Member Function Documentation

◆ output_indices()

template<int dim>

void TensorProductPolynomialsBubbles< dim >::output_indices ( std::ostream & out ) const

Print the list of tensor_polys indices to out.

Definition at line 31 of file tensor_product_polynomials_bubbles.cc.

◆ set_numbering()

template<int dim>

void TensorProductPolynomialsBubbles< dim >::set_numbering ( const std::vector< unsigned int > & renumber )

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

Definition at line 48 of file tensor_product_polynomials_bubbles.cc.

◆ get_numbering()

template<int dim>

const std::vector<unsigned int>& TensorProductPolynomialsBubbles< dim >::get_numbering ( ) const

Give read access to the renumber vector.

◆ get_numbering_inverse()

template<int dim>

const std::vector<unsigned int>& TensorProductPolynomialsBubbles< dim >::get_numbering_inverse ( ) const

Give read access to the inverse renumber vector.

◆ evaluate()

template<int dim>

void TensorProductPolynomialsBubbles< dim >::evaluate	(	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

override

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 257 of file tensor_product_polynomials_bubbles.cc.

◆ compute_value() [1/2]

template<int dim>

double TensorProductPolynomialsBubbles< 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 evaluate() 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 68 of file tensor_product_polynomials_bubbles.cc.

◆ compute_derivative()

template<int dim>

template<int order>

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

Compute the order order 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 evaluate() 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.

◆ compute_grad()

template<int dim>

Tensor< 1, dim > TensorProductPolynomialsBubbles< 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 evaluate() 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 107 of file tensor_product_polynomials_bubbles.cc.

◆ compute_grad_grad()

template<int dim>

Tensor< 2, dim > TensorProductPolynomialsBubbles< 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 evaluate() 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 153 of file tensor_product_polynomials_bubbles.cc.

◆ n()

template<int dim>

unsigned int TensorProductPolynomialsBubbles< dim >::n ( ) const

Return the number of tensor product polynomials plus the bubble enrichments. For n 1d polynomials this is n^dim+1 if the maximum degree of the polynomials is one and n^dim+dim otherwise.

◆ name()

template<int dim>

std::string TensorProductPolynomialsBubbles< dim >::name ( ) const

override

Return the name of the space, which is TensorProductPolynomialsBubbles.

◆ clone()

template<int dim>

std::unique_ptr< ScalarPolynomialsBase< dim > > TensorProductPolynomialsBubbles< dim >::clone

overridevirtual

A sort of virtual copy constructor, this function returns a copy of the polynomial space object. Derived classes need to override the function here in this base class and return an object of the same type as the derived class.

Some places in the library, for example the constructors of FE_Poly, need to make copies of polynomial spaces without knowing their exact type. They do so through this function.

Definition at line 337 of file tensor_product_polynomials_bubbles.cc.