Reference documentation for deal.II version GIT relicensing-750-gcfa4c29382 2024-05-25 07:20:02+00:00
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Public Member Functions | Private Member Functions | Static Private Member Functions | List of all members
QGaussLog< dim > Class Template Reference

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

Inheritance diagram for QGaussLog< dim >:
Inheritance graph
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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.

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.


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