Reference documentation for deal.II version GIT relicensing-750-gcfa4c29382 2024-05-25 07:20:02+00:00
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QGaussLog< dim > Class Template Reference

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

Inheritance diagram for QGaussLog< dim >:
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## 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.

## ◆ 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

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

Compute the points of the quadrature formula.

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

Compute the weights of the quadrature formula.

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

Definition at line 503 of file quadrature_lib.cc.