Reference documentation for deal.II version GIT c9976103bc 2022-12-09 17:30:02+00:00
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Public Types | Public Member Functions | Static Public Member Functions | Static Public Attributes | Protected Attributes | Private Attributes | List of all members
BarycentricPolynomials< dim > Class Template Reference

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

Inheritance diagram for BarycentricPolynomials< dim >:
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Public Types

using PolyType = BarycentricPolynomial< dim >
 
using GradType = std::array< PolyType, dim >
 
using HessianType = std::array< GradType, dim >
 
using ThirdDerivativesType = std::array< HessianType, dim >
 
using FourthDerivativesType = std::array< ThirdDerivativesType, dim >
 

Public Member Functions

 BarycentricPolynomials (const std::vector< BarycentricPolynomial< dim >> &polynomials)
 
const BarycentricPolynomial< dim > & operator[] (const std::size_t i) 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
 
Tensor< 1, dim > compute_1st_derivative (const unsigned int i, const Point< dim > &p) const override
 
Tensor< 2, dim > compute_2nd_derivative (const unsigned int i, const Point< dim > &p) const override
 
Tensor< 3, dim > compute_3rd_derivative (const unsigned int i, const Point< dim > &p) const override
 
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
 
virtual std::size_t memory_consumption () const override
 
std::string name () const override
 
virtual std::unique_ptr< ScalarPolynomialsBase< dim > > clone () const override
 
template<int order>
Tensor< order, dim > compute_derivative (const unsigned int i, const Point< dim > &p) const
 
unsigned int n () const
 
virtual unsigned int degree () const
 

Static Public Member Functions

static BarycentricPolynomials< dim > get_fe_p_basis (const unsigned int degree)
 

Static Public Attributes

static constexpr unsigned int dimension = dim
 

Protected Attributes

std::vector< PolyTypepolys
 
std::vector< GradTypepoly_grads
 
std::vector< HessianTypepoly_hessians
 
std::vector< ThirdDerivativesTypepoly_third_derivatives
 
std::vector< FourthDerivativesTypepoly_fourth_derivatives
 

Private Attributes

const unsigned int polynomial_degree
 
const unsigned int n_pols
 

Detailed Description

template<int dim>
class BarycentricPolynomials< dim >

Scalar polynomial space based on barycentric polynomials.

Definition at line 217 of file polynomials_barycentric.h.

Member Typedef Documentation

◆ PolyType

template<int dim>
using BarycentricPolynomials< dim >::PolyType = BarycentricPolynomial<dim>

Alias for polynomial type.

Definition at line 223 of file polynomials_barycentric.h.

◆ GradType

template<int dim>
using BarycentricPolynomials< dim >::GradType = std::array<PolyType, dim>

Alias for polynomial gradient type.

Definition at line 228 of file polynomials_barycentric.h.

◆ HessianType

template<int dim>
using BarycentricPolynomials< dim >::HessianType = std::array<GradType, dim>

Alias for polynomial hessian type.

Definition at line 233 of file polynomials_barycentric.h.

◆ ThirdDerivativesType

template<int dim>
using BarycentricPolynomials< dim >::ThirdDerivativesType = std::array<HessianType, dim>

Alias for polynomial third derivatives type.

Definition at line 238 of file polynomials_barycentric.h.

◆ FourthDerivativesType

template<int dim>
using BarycentricPolynomials< dim >::FourthDerivativesType = std::array<ThirdDerivativesType, dim>

Alias for polynomial fourth derivatives type.

Definition at line 243 of file polynomials_barycentric.h.

Constructor & Destructor Documentation

◆ BarycentricPolynomials()

template<int dim>
BarycentricPolynomials< dim >::BarycentricPolynomials ( const std::vector< BarycentricPolynomial< dim >> &  polynomials)

Constructor taking the polynomial degree as input.

Definition at line 105 of file polynomials_barycentric.cc.

Member Function Documentation

◆ get_fe_p_basis()

template<int dim>
BarycentricPolynomials< dim > BarycentricPolynomials< dim >::get_fe_p_basis ( const unsigned int  degree)
static

Get the standard Lagrange basis for a specified degree.

Definition at line 59 of file polynomials_barycentric.cc.

◆ operator[]()

template<int dim>
const BarycentricPolynomial< dim > & BarycentricPolynomials< dim >::operator[] ( const std::size_t  i) const

Access operator.

Definition at line 727 of file polynomials_barycentric.h.

◆ evaluate()

template<int dim>
void BarycentricPolynomials< 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 derivatives of the polynomials at unit_point.

The size of the vectors must either be zero or equal n(). In the first case, the function will not compute these values.

If you need values or derivatives of all 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 149 of file polynomials_barycentric.cc.

◆ compute_value()

template<int dim>
double BarycentricPolynomials< dim >::compute_value ( const unsigned int  i,
const Point< dim > &  p 
) const
overridevirtual

Compute the value of the ith polynomial at unit point p.

Consider using evaluate() instead.

Implements ScalarPolynomialsBase< dim >.

Definition at line 208 of file polynomials_barycentric.cc.

◆ compute_1st_derivative()

template<int dim>
Tensor< 1, dim > BarycentricPolynomials< 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 >.

Definition at line 219 of file polynomials_barycentric.cc.

◆ compute_2nd_derivative()

template<int dim>
Tensor< 2, dim > BarycentricPolynomials< 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 >.

Definition at line 232 of file polynomials_barycentric.cc.

◆ compute_3rd_derivative()

template<int dim>
Tensor< 3, dim > BarycentricPolynomials< 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 >.

Definition at line 247 of file polynomials_barycentric.cc.

◆ compute_4th_derivative()

template<int dim>
Tensor< 4, dim > BarycentricPolynomials< 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 >.

Definition at line 263 of file polynomials_barycentric.cc.

◆ compute_grad()

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

Compute the gradient of the ith polynomial at unit point p.

Consider using evaluate() instead.

Implements ScalarPolynomialsBase< dim >.

Definition at line 281 of file polynomials_barycentric.cc.

◆ compute_grad_grad()

template<int dim>
Tensor< 2, dim > BarycentricPolynomials< dim >::compute_grad_grad ( const unsigned int  i,
const Point< dim > &  p 
) const
overridevirtual

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

Consider using evaluate() instead.

Implements ScalarPolynomialsBase< dim >.

Definition at line 291 of file polynomials_barycentric.cc.

◆ memory_consumption()

template<int dim>
std::size_t BarycentricPolynomials< dim >::memory_consumption
overridevirtual

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

Reimplemented from ScalarPolynomialsBase< dim >.

Definition at line 319 of file polynomials_barycentric.cc.

◆ name()

template<int dim>
std::string BarycentricPolynomials< dim >::name
overridevirtual

Return the name of the space.

Implements ScalarPolynomialsBase< dim >.

Definition at line 310 of file polynomials_barycentric.cc.

◆ clone()

template<int dim>
std::unique_ptr< ScalarPolynomialsBase< dim > > BarycentricPolynomials< 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 301 of file polynomials_barycentric.cc.

◆ compute_derivative()

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

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

Consider using evaluate() instead.

Template Parameters
orderThe order of the derivative.

Definition at line 259 of file scalar_polynomials_base.h.

◆ n()

template<int dim>
unsigned int ScalarPolynomialsBase< dim >::n
inlineinherited

Return the number of polynomials.

Definition at line 240 of file scalar_polynomials_base.h.

◆ 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.

Member Data Documentation

◆ dimension

template<int dim>
constexpr unsigned int BarycentricPolynomials< dim >::dimension = dim
staticconstexpr

Make the dimension available to the outside.

Definition at line 248 of file polynomials_barycentric.h.

◆ polys

template<int dim>
std::vector<PolyType> BarycentricPolynomials< dim >::polys
protected

Definition at line 344 of file polynomials_barycentric.h.

◆ poly_grads

template<int dim>
std::vector<GradType> BarycentricPolynomials< dim >::poly_grads
protected

Definition at line 345 of file polynomials_barycentric.h.

◆ poly_hessians

template<int dim>
std::vector<HessianType> BarycentricPolynomials< dim >::poly_hessians
protected

Definition at line 346 of file polynomials_barycentric.h.

◆ poly_third_derivatives

template<int dim>
std::vector<ThirdDerivativesType> BarycentricPolynomials< dim >::poly_third_derivatives
protected

Definition at line 347 of file polynomials_barycentric.h.

◆ poly_fourth_derivatives

template<int dim>
std::vector<FourthDerivativesType> BarycentricPolynomials< dim >::poly_fourth_derivatives
protected

Definition at line 348 of file polynomials_barycentric.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: