QGaussLog< dim > Class Template Reference

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

Inheritance diagram for QGaussLog< dim >:

Public Member Functions
	QGaussLog (const unsigned int n, const bool revert=false)
Public Member Functions inherited from Quadrature< dim >
	Quadrature (const unsigned int n_quadrature_points=0)
	Quadrature (const SubQuadrature &, const Quadrature< 1 > &)
	Quadrature (const Quadrature< dim !=1 ? 1 :0 > &quadrature_1d)
	Quadrature (const Quadrature< dim > &q)
	Quadrature (Quadrature< dim > &&) noexcept=default
	Quadrature (const std::vector< Point< dim > > &points, const std::vector< double > &weights)
	Quadrature (const std::vector< Point< dim > > &points)
	Quadrature (const Point< dim > &point)
virtual	~Quadrature ()=default
Quadrature &	operator= (const Quadrature< dim > &)
Quadrature &	operator= (Quadrature< dim > &&)=default
bool	operator== (const Quadrature< dim > &p) const
void	initialize (const std::vector< Point< dim > > &points, const std::vector< double > &weights)
unsigned int	size () const
const Point< dim > &	point (const unsigned int i) const
const std::vector< Point< dim > > &	get_points () const
double	weight (const unsigned int i) const
const std::vector< double > &	get_weights () const
std::size_t	memory_consumption () const
template<class Archive >
void	serialize (Archive &ar, const unsigned int version)
bool	is_tensor_product () const
std::conditional< dim==1, std::array< Quadrature< 1 >, dim >, const std::array< Quadrature< 1 >, dim > & >::type	get_tensor_basis () const
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
void	list_subscribers () const
template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

Static Private Member Functions
static std::vector< double >	get_quadrature_points (const unsigned int n)
static std::vector< double >	get_quadrature_weights (const unsigned int n)

Additional Inherited Members
Public Types inherited from Quadrature< dim >
typedef Quadrature< dim-1 >	SubQuadrature
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)
Protected Attributes inherited from Quadrature< dim >
std::vector< Point< dim > >	quadrature_points
std::vector< double >	weights
bool	is_tensor_product_flag
std::unique_ptr< std::array< Quadrature< 1 >, dim > >	tensor_basis

Detailed Description

template<int dim>
class QGaussLog< dim >

A class for Gauss quadrature with logarithmic weighting function. This formula is used to integrate \(\ln|x|\;f(x)\) on the interval \([0,1]\), where \(f\) is a smooth function without singularities. The collection of quadrature points and weights has been obtained using Numerical Recipes.

Notice that only the function \(f(x)\) should be provided, i.e., \(\int_0^1 f(x) \ln|x| dx = \sum_{i=0}^N w_i f(q_i)\). Setting the revert flag to true at construction time switches the weight from \(\ln|x|\) to \(\ln|1-x|\).

The weights and functions have been tabulated up to order 12.

Definition at line 176 of file quadrature_lib.h.

Constructor & Destructor Documentation

QGaussLog()

template<int dim>

QGaussLog< dim >::QGaussLog	(	const unsigned int	n,
		const bool	revert = false
	)

Generate a formula with n quadrature points

Member Function Documentation

get_quadrature_points()

template<int dim>

static std::vector<double> QGaussLog< dim >::get_quadrature_points ( const unsigned int  n )

staticprivate

Compute the points of the quadrature formula.

get_quadrature_weights()

template<int dim>

static std::vector<double> QGaussLog< dim >::get_quadrature_weights ( const unsigned int  n )

staticprivate

Compute the weights of the quadrature formula.

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

• deal.II/base/quadrature_lib.h