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)
	QGaussLog (const unsigned int n, const bool revert)

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

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)

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 240 of file quadrature_lib.h.

Constructor & Destructor Documentation

QGaussLog() [1/2]

template<int dim>

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

Generate a formula with n quadrature points

QGaussLog() [2/2]

QGaussLog< 1 >::QGaussLog	(	const unsigned int	n,
		const bool	revert
	)

Definition at line 484 of file quadrature_lib.cc.

Member Function Documentation

get_quadrature_points() [1/2]

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() [1/2]

template<int dim>

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

staticprivate

Compute the weights of the quadrature formula.

get_quadrature_points() [2/2]

std::vector< double > QGaussLog< 1 >::get_quadrature_points ( const unsigned int  n )

private

Definition at line 503 of file quadrature_lib.cc.

get_quadrature_weights() [2/2]

std::vector< double > QGaussLog< 1 >::get_quadrature_weights ( const unsigned int  n )

private

Definition at line 636 of file quadrature_lib.cc.

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

• include/deal.II/base/quadrature_lib.h