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	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
std::string	name () const override
virtual std::unique_ptr< ScalarPolynomialsBase< dim > >	clone () const override
virtual std::size_t	memory_consumption () const override
std::vector< PolynomialType >	get_underlying_polynomials () const
void	output_indices (std::ostream &) const
void	set_numbering (const std::vector< unsigned int > &)
double	compute_value (const unsigned int, const Point< 0 > &) const
Tensor< 1, 0 >	compute_grad (const unsigned int, const Point< 0 > &) const
Tensor< 2, 0 >	compute_grad_grad (const unsigned int, const Point< 0 > &) const
void	evaluate (const Point< 0 > &, std::vector< double > &, std::vector< Tensor< 1, 0 > > &, std::vector< Tensor< 2, 0 > > &, std::vector< Tensor< 3, 0 > > &, std::vector< Tensor< 4, 0 > > &) const
unsigned int	n () const
virtual unsigned int	degree () const

Static Public Attributes
static constexpr unsigned int	dimension = dim

Protected Member Functions
void	compute_index (const unsigned int i, std::array< unsigned int, dim > &indices) const
void	compute_index (const unsigned int, std::array< unsigned int, 0 > &) const

Protected Attributes
std::vector< PolynomialType >	polynomials
std::vector< unsigned int >	index_map
std::vector< unsigned int >	index_map_inverse

Private Attributes
const unsigned int	polynomial_degree
const unsigned int	n_pols

Friends
class	TensorProductPolynomialsBubbles< dim >
class	TensorProductPolynomialsConst< dim >

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.

Template Parameters

PolynomialType

A class that satisfies the required interface for computing tensor products. Typical choices for this template argument are Polynomials::Polynomial and Polynomials::PiecewisePolynomial.

Definition at line 75 of file tensor_product_polynomials.h.

Constructor & Destructor Documentation

TensorProductPolynomials()

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 protected member variable.

Member Function Documentation

output_indices() [1/2]

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 110 of file tensor_product_polynomials.cc.

set_numbering() [1/2]

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 180 of file tensor_product_polynomials.cc.

get_numbering()

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.

get_numbering_inverse()

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.

evaluate() [1/2]

template<int dim, typename PolynomialType >

void TensorProductPolynomials< dim, PolynomialType >::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 542 of file tensor_product_polynomials.cc.

compute_value() [1/2]

template<int dim, typename PolynomialType >

double TensorProductPolynomials< dim, PolynomialType >::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 205 of file tensor_product_polynomials.cc.

compute_derivative()

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 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.

Template Parameters

order

The derivative order.

compute_1st_derivative()

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

virtual Tensor< 1, dim > TensorProductPolynomials< dim, PolynomialType >::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, typename PolynomialType = Polynomials::Polynomial<double>>

virtual Tensor< 2, dim > TensorProductPolynomials< dim, PolynomialType >::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, typename PolynomialType = Polynomials::Polynomial<double>>

virtual Tensor< 3, dim > TensorProductPolynomials< dim, PolynomialType >::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, typename PolynomialType = Polynomials::Polynomial<double>>

virtual Tensor< 4, dim > TensorProductPolynomials< dim, PolynomialType >::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() [1/2]

template<int dim, typename PolynomialType >

Tensor< 1, dim > TensorProductPolynomials< dim, PolynomialType >::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 238 of file tensor_product_polynomials.cc.

compute_grad_grad() [1/2]

template<int dim, typename PolynomialType >

Tensor< 2, dim > TensorProductPolynomials< dim, PolynomialType >::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 288 of file tensor_product_polynomials.cc.

name()

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

std::string TensorProductPolynomials< dim, PolynomialType >::name ( ) const

overridevirtual

Return the name of the space, which is TensorProductPolynomials.

Implements ScalarPolynomialsBase< dim >.

clone()

template<int dim, typename PolynomialType >

std::unique_ptr< ScalarPolynomialsBase< dim > > TensorProductPolynomials< dim, PolynomialType >::clone ( ) const

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 652 of file tensor_product_polynomials.cc.

memory_consumption()

template<int dim, typename PolynomialType >

std::size_t TensorProductPolynomials< dim, PolynomialType >::memory_consumption ( ) const

overridevirtual

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

Reimplemented from ScalarPolynomialsBase< dim >.

Definition at line 661 of file tensor_product_polynomials.cc.

get_underlying_polynomials()

template<int dim, typename PolynomialType >

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

(

)

const

Return a copy of the underlying one-dimensional polynomials given to the constructor of this class.

Definition at line 672 of file tensor_product_polynomials.cc.

compute_index() [1/2]

template<int dim, typename PolynomialType >

void TensorProductPolynomials< dim, PolynomialType >::compute_index ( const unsigned int i, std::array< unsigned int, dim > & indices ) 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 83 of file tensor_product_polynomials.cc.

compute_index() [2/2]

void TensorProductPolynomials< 0, Polynomials::Polynomial< double > >::compute_index ( const unsigned int , std::array< unsigned int, 0 > &  ) const

inlineprotected

Definition at line 99 of file tensor_product_polynomials.cc.

output_indices() [2/2]

void TensorProductPolynomials< 0, Polynomials::Polynomial< double > >::output_indices

(

std::ostream &

)

const

Definition at line 128 of file tensor_product_polynomials.cc.

set_numbering() [2/2]

void TensorProductPolynomials< 0, Polynomials::Polynomial< double > >::set_numbering

(

const std::vector< unsigned int > &

)

Definition at line 195 of file tensor_product_polynomials.cc.

compute_value() [2/2]

double TensorProductPolynomials< 0, Polynomials::Polynomial< double > >::compute_value	(	const unsigned int	,
		const Point< 0 > &	) const

Definition at line 225 of file tensor_product_polynomials.cc.

compute_grad() [2/2]

Tensor< 1, 0 > TensorProductPolynomials< 0, Polynomials::Polynomial< double > >::compute_grad	(	const unsigned int	,
		const Point< 0 > &	) const

Definition at line 275 of file tensor_product_polynomials.cc.

compute_grad_grad() [2/2]

Tensor< 2, 0 > TensorProductPolynomials< 0, Polynomials::Polynomial< double > >::compute_grad_grad	(	const unsigned int	,
		const Point< 0 > &	) const

Definition at line 333 of file tensor_product_polynomials.cc.

evaluate() [2/2]

void TensorProductPolynomials< 0, Polynomials::Polynomial< double > >::evaluate	(	const Point< 0 > &	,
		std::vector< double > &	,
		std::vector< Tensor< 1, 0 > > &	,
		std::vector< Tensor< 2, 0 > > &	,
		std::vector< Tensor< 3, 0 > > &	,
		std::vector< Tensor< 4, 0 > > &	) const

Definition at line 637 of file tensor_product_polynomials.cc.

n()

template<int dim>

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

inlineinherited

Return the number of polynomials.

Definition at line 239 of file scalar_polynomials_base.h.

degree()

template<int dim>

unsigned int ScalarPolynomialsBase< dim >::degree ( ) const

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 248 of file scalar_polynomials_base.h.

Friends And Related Symbol Documentation

TensorProductPolynomialsBubbles< dim >

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

friend class TensorProductPolynomialsBubbles< dim >

friend

TensorProductPolynomialsBubbles has a TensorProductPolynomials class so we declare it as a friend class.

Definition at line 277 of file tensor_product_polynomials.h.

TensorProductPolynomialsConst< dim >

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

friend class TensorProductPolynomialsConst< dim >

friend

TensorProductPolynomialsConst has a TensorProductPolynomials class so we declare it as a friend class.

Definition at line 277 of file tensor_product_polynomials.h.

Member Data Documentation

dimension

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

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

staticconstexpr

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

Definition at line 82 of file tensor_product_polynomials.h.

polynomials

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 258 of file tensor_product_polynomials.h.

index_map

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 263 of file tensor_product_polynomials.h.

index_map_inverse

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 268 of file tensor_product_polynomials.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 227 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 232 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
• source/base/tensor_product_polynomials.cc