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

Inheritance diagram for IntegratedLegendreSZ:

Public Member Functions
	IntegratedLegendreSZ (const unsigned int p)

Public Member Functions inherited from Polynomials::Polynomial< double >
	Polynomial (const std::vector< double > &coefficients)

	Polynomial (const unsigned int n)

	Polynomial (const std::vector< Point< 1 >> &lagrange_support_points, const unsigned int evaluation_point)

	Polynomial ()

double	value (const doublex) const

void	value (const doublex, std::vector< double > &values) const

void	value (const doublex, const unsigned int n_derivatives, double *values) const

unsigned int	degree () const

void	scale (const doublefactor)

void	shift (const number2 offset)

Polynomial< double >	derivative () const

Polynomial< double >	primitive () const

Polynomial< double > &	operator*= (const double s)

Polynomial< double > &	operator*= (const Polynomial< double > &p)

Polynomial< double > &	operator+= (const Polynomial< double > &p)

Polynomial< double > &	operator-= (const Polynomial< double > &p)

bool	operator== (const Polynomial< double > &p) const

void	print (std::ostream &out) const

void	serialize (Archive &ar, const unsigned int version)

Public Member Functions inherited from Subscriptor
	Subscriptor ()

	Subscriptor (const Subscriptor &)

	Subscriptor (Subscriptor &&) noexcept

virtual	~Subscriptor ()

Subscriptor &	operator= (const Subscriptor &)

Subscriptor &	operator= (Subscriptor &&) noexcept

void	subscribe (const char *identifier=nullptr) const

void	unsubscribe (const char *identifier=nullptr) const

unsigned int	n_subscriptions () const

template<typename StreamType >
void	list_subscribers (StreamType &stream) const

void	list_subscribers () const

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

Static Public Member Functions
static std::vector< Polynomials::Polynomial< double > >	generate_complete_basis (const unsigned int degree)

Static Public Member Functions inherited from Subscriptor
static::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

static::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string arg2)

Static Private Member Functions
static const std::vector< double >	get_coefficients (const unsigned int k)

Additional Inherited Members
Protected Member Functions inherited from Polynomials::Polynomial< double >
void	transform_into_standard_form ()

Static Protected Member Functions inherited from Polynomials::Polynomial< double >
static void	scale (std::vector< double > &coefficients, const doublefactor)

static void	shift (std::vector< double > &coefficients, const number2 shift)

static void	multiply (std::vector< double > &coefficients, const doublefactor)

Protected Attributes inherited from Polynomials::Polynomial< double >
std::vector< double >	coefficients

bool	in_lagrange_product_form

std::vector< double >	lagrange_support_points

double	lagrange_weight

Detailed Description

Class implementing the integrated Legendre polynomials described in the PhD thesis of Sabine Zaglmayr.

This class was written based upon the existing deal.II Legendre class as a base, but with the coefficients adjusted so that the recursive formula is for the integrated Legendre polynomials described in the PhD thesis of Sabine Zaglmayr. The polynomials can be generated recursively from:

\(L_{0}(x) = -1\) (added so that it can be generated recursively from 0)
\(L_{1}(x) = x\)
\(L_{2}(x) = \frac{(x^2 - 1)}{2}\)
\((n+1)L_{n+1} = (2n-1)L_{n} - (n-2)L_{n-1}\).

However, it is also possible to generate them directly from the Legendre polynomials:

\(L_{n} = \frac{l_{n} - l_{n-2}}{2n-1)}\)

Definition at line 49 of file polynomials_integrated_legendre_sz.h.

Constructor & Destructor Documentation

IntegratedLegendreSZ::IntegratedLegendreSZ ( const unsigned int p )

Constructor generating the coefficients of the polynomials at degree p.

Definition at line 21 of file polynomials_integrated_legendre_sz.cc.

Member Function Documentation

std::vector< Polynomials::Polynomial< double > > IntegratedLegendreSZ::generate_complete_basis ( const unsigned int degree )

static

Return the complete set of Integrated Legendre polynomials up to the given degree.

Definition at line 76 of file polynomials_integrated_legendre_sz.cc.

const std::vector< double > IntegratedLegendreSZ::get_coefficients ( const unsigned int k )

staticprivate

Main function to compute the co-efficients of the polynomial at degree p.

Definition at line 28 of file polynomials_integrated_legendre_sz.cc.

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

deal.II/base/polynomials_integrated_legendre_sz.h
/mnt/data/darndt/Sources/dealii-clang-6.0.0/source/base/polynomials_integrated_legendre_sz.cc

Public Member Functions

Static Public Member Functions

Static Private Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation