Reference documentation for deal.II version GIT relicensing-1401-g878ed2bce2 2024-08-10 16:00:02+00:00
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QGaussRadauChebyshev< dim > Class Template Reference

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

Inheritance diagram for QGaussRadauChebyshev< dim >:
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## Public Types

enum  EndPoint { left , right }

## Public Member Functions

Generate a formula with n quadrature points.

QGaussRadauChebyshev (const unsigned int n, const EndPoint end_point)

## Private Attributes

const EndPoint end_point

## Detailed Description

template<int dim>

Gauss-Radau-Chebyshev quadrature rules integrate the weighted product $$\int_{-1}^1 f(x) w(x) dx$$ with weight given by: $$w(x) = 1/\sqrt{1-x^2}$$ with the additional constraint that a quadrature point lies at one of the two extrema of the interval. The nodes and weights are known analytically, and are exact for monomials up to the order $$2n-2$$, where $$n$$ is the number of quadrature points. Here we rescale the quadrature formula so that it is defined on the interval $$[0,1]$$ instead of $$[-1,1]$$. So the quadrature formulas integrate exactly the integral $$\int_0^1 f(x) w(x) dx$$ with the weight: $$w(x) = 1/\sqrt{x(1-x)}$$. By default the quadrature is constructed with the left endpoint as quadrature node, but the quadrature node can be imposed at the right endpoint through the variable ep that can assume the values left or right.

Definition at line 581 of file quadrature_lib.h.

## ◆ EndPoint

template<int dim>

EndPoint is used to specify which of the two endpoints of the unit interval is used also as quadrature point.

Enumerator
left

Left end point.

right

Right end point.

Definition at line 588 of file quadrature_lib.h.

## Constructor & Destructor Documentation

template<int dim>
 QGaussRadauChebyshev< dim >::QGaussRadauChebyshev ( const unsigned int n, const EndPoint end_point = QGaussRadauChebyshev< dim >::EndPoint::left )

Generate a formula with n quadrature points.

Definition at line 1366 of file quadrature_lib.cc.

template<int dim>
defaultnoexcept

Move constructor.

 QGaussRadauChebyshev< 1 >::QGaussRadauChebyshev ( const unsigned int n, const EndPoint end_point )

Definition at line 1346 of file quadrature_lib.cc.

## ◆ end_point

template<int dim>