Reference documentation for deal.II version Git 35565f205e 2019-09-24 08:33:37 +0200
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Public Member Functions | Static Public Attributes | Protected Member Functions | Protected Attributes | Friends | List of all members
TensorProductPolynomials< dim, PolynomialType > Class Template Reference

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

Inheritance diagram for TensorProductPolynomials< dim, PolynomialType >:
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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
 
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
 
std::string name () const override
 
virtual std::unique_ptr< ScalarPolynomialsBase< dim > > clone () const override
 
- Public Member Functions inherited from ScalarPolynomialsBase< dim >
 ScalarPolynomialsBase (const unsigned int deg, const unsigned int n_polynomials)
 
 ScalarPolynomialsBase (ScalarPolynomialsBase< dim > &&)=default
 
 ScalarPolynomialsBase (const ScalarPolynomialsBase< dim > &)=default
 
virtual ~ScalarPolynomialsBase ()=default
 
unsigned int n () const
 
unsigned int degree () 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
 
std::vector< unsigned int > index_map
 
std::vector< unsigned int > index_map_inverse
 

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 Pn, this class generates ndim polynomials of the form Qijk(x,y,z) = Pi(x)Pj(y)Pk(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 74 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 private variable.

Member Function Documentation

◆ output_indices()

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.

◆ set_numbering()

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.

◆ 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()

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 267 of file tensor_product_polynomials.cc.

◆ compute_value()

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.

◆ 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 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
orderThe derivative order.

◆ compute_grad()

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.

◆ compute_grad_grad()

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 211 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 430 of file tensor_product_polynomials.cc.

◆ compute_index()

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.

Friends And Related Function 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 243 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 249 of file tensor_product_polynomials.h.

Member Data Documentation

◆ dimension

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 81 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 216 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 221 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 226 of file tensor_product_polynomials.h.


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