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

Inheritance diagram for TensorProductPolynomialsBubbles< dim >:

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 override

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

virtual Tensor< 1, dim >	compute_1st_derivative (const unsigned int i, const Point< dim > &p) const override

virtual Tensor< 2, dim >	compute_2nd_derivative (const unsigned int i, const Point< dim > &p) const override

virtual Tensor< 3, dim >	compute_3rd_derivative (const unsigned int i, const Point< dim > &p) const override

virtual Tensor< 4, dim >	compute_4th_derivative (const unsigned int i, const Point< dim > &p) const override

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

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

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

virtual unsigned int	degree () const

virtual std::size_t	memory_consumption () const

Static Public Attributes
static constexpr unsigned int	dimension = dim

Private Attributes
TensorProductPolynomials< dim >	tensor_polys

std::vector< unsigned int >	index_map

std::vector< unsigned int >	index_map_inverse

const unsigned int	polynomial_degree

const unsigned int	n_pols

Detailed Description

template<int dim>
class TensorProductPolynomialsBubbles< dim >

A class that represents a space of tensor product polynomials, augmented by \(dim\) (non-normalized) bubble functions of form \(\varphi_j(\mathbf x) = 2^{\text{degree}-1}\left(x_j-frac 12\right)^{\text{degree}-1} \left[\prod_{i=0}^{dim-1}(x_i(1-x_i))\right]\) for \(j=0,\ldots,dim-1\). If degree is one, then the first factor disappears and one receives the usual bubble function centered at the mid-point of the cell.

This class inherits most of its functionality from TensorProductPolynomials. The bubble enrichments are added for the last index.

Definition at line 53 of file tensor_product_polynomials_bubbles.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 32 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 49 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

overridevirtual

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.

Implements ScalarPolynomialsBase< dim >.

Definition at line 260 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

overridevirtual

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.

Implements ScalarPolynomialsBase< dim >.

Definition at line 69 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_1st_derivative()

template<int dim>

virtual Tensor< 1, dim > TensorProductPolynomialsBubbles< dim >::compute_1st_derivative	(	const unsigned int	i,
		const Point< dim > &	p
	)		const

overridevirtual

Compute the first derivative of the ith polynomial at unit point p.

Consider using evaluate() instead.

Implements ScalarPolynomialsBase< dim >.

◆ compute_2nd_derivative()

template<int dim>

virtual Tensor< 2, dim > TensorProductPolynomialsBubbles< dim >::compute_2nd_derivative	(	const unsigned int	i,
		const Point< dim > &	p
	)		const

overridevirtual

Compute the second derivative of the ith polynomial at unit point p.

Consider using evaluate() instead.

Implements ScalarPolynomialsBase< dim >.

◆ compute_3rd_derivative()

template<int dim>

virtual Tensor< 3, dim > TensorProductPolynomialsBubbles< dim >::compute_3rd_derivative	(	const unsigned int	i,
		const Point< dim > &	p
	)		const

overridevirtual

Compute the third derivative of the ith polynomial at unit point p.

Consider using evaluate() instead.

Implements ScalarPolynomialsBase< dim >.

◆ compute_4th_derivative()

template<int dim>

virtual Tensor< 4, dim > TensorProductPolynomialsBubbles< dim >::compute_4th_derivative	(	const unsigned int	i,
		const Point< dim > &	p
	)		const

overridevirtual

Compute the fourth derivative of the ith polynomial at unit point p.

Consider using evaluate() instead.

Implements ScalarPolynomialsBase< dim >.

◆ compute_grad()

template<int dim>

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

overridevirtual

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.

Implements ScalarPolynomialsBase< dim >.

Definition at line 110 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

overridevirtual

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.

Implements ScalarPolynomialsBase< dim >.

Definition at line 156 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

overridevirtual

Return the name of the space, which is TensorProductPolynomialsBubbles.

Implements ScalarPolynomialsBase< dim >.

◆ 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.

Implements ScalarPolynomialsBase< dim >.

Definition at line 340 of file tensor_product_polynomials_bubbles.cc.

◆ compute_value() [2/2]

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

Definition at line 99 of file tensor_product_polynomials_bubbles.cc.

◆ degree()

template<int dim>

unsigned int ScalarPolynomialsBase< dim >::degree

inlinevirtualinherited

Return the highest polynomial degree of polynomials represented by this class. A derived class may override this if its value is different from my_degree.

Reimplemented in PolynomialsP< dim >.

Definition at line 249 of file scalar_polynomials_base.h.

◆ memory_consumption()

template<int dim>

std::size_t ScalarPolynomialsBase< dim >::memory_consumption

virtualinherited

Return an estimate (in bytes) for the memory consumption of this object.

Reimplemented in BarycentricPolynomials< dim >, BarycentricPolynomials< 1 >, BarycentricPolynomials< 2 >, TensorProductPolynomials< dim, PolynomialType >, and TensorProductPolynomials< dim - 1 >.

Definition at line 39 of file scalar_polynomials_base.cc.

Member Data Documentation

◆ dimension

template<int dim>

constexpr unsigned int TensorProductPolynomialsBubbles< dim >::dimension = dim

staticconstexpr

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

Definition at line 60 of file tensor_product_polynomials_bubbles.h.

◆ tensor_polys

template<int dim>

TensorProductPolynomials<dim> TensorProductPolynomialsBubbles< dim >::tensor_polys

private

The TensorProductPolynomials object

Definition at line 231 of file tensor_product_polynomials_bubbles.h.

◆ index_map

template<int dim>

std::vector<unsigned int> TensorProductPolynomialsBubbles< dim >::index_map

private

Index map for reordering the polynomials.

Definition at line 236 of file tensor_product_polynomials_bubbles.h.

◆ index_map_inverse

template<int dim>

std::vector<unsigned int> TensorProductPolynomialsBubbles< dim >::index_map_inverse

private

Index map for reordering the polynomials.

Definition at line 241 of file tensor_product_polynomials_bubbles.h.

◆ polynomial_degree

template<int dim>

const unsigned int ScalarPolynomialsBase< dim >::polynomial_degree

privateinherited

The highest polynomial degree of this functions represented by this object.

Definition at line 228 of file scalar_polynomials_base.h.

◆ n_pols

template<int dim>

const unsigned int ScalarPolynomialsBase< dim >::n_pols

privateinherited

The number of polynomials represented by this object.

Definition at line 233 of file scalar_polynomials_base.h.

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

include/deal.II/base/tensor_product_polynomials.h
include/deal.II/base/tensor_product_polynomials_bubbles.h
source/base/tensor_product_polynomials_bubbles.cc

Public Member Functions

Static Public Attributes

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ TensorProductPolynomialsBubbles()

Member Function Documentation

◆ output_indices()

◆ set_numbering()

◆ get_numbering()

◆ get_numbering_inverse()

◆ evaluate()

◆ compute_value() [1/2]

◆ compute_derivative()

◆ compute_1st_derivative()

◆ compute_2nd_derivative()

◆ compute_3rd_derivative()

◆ compute_4th_derivative()

◆ compute_grad()

◆ compute_grad_grad()

◆ n()

◆ name()

◆ clone()

◆ compute_value() [2/2]

◆ degree()

◆ memory_consumption()

Member Data Documentation

◆ dimension

◆ tensor_polys

◆ index_map

◆ index_map_inverse

◆ polynomial_degree

◆ n_pols