Reference documentation for deal.II version GIT relicensing-1291-gf3a46e514e 2024-07-24 11:20:02+00:00
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QGaussLobattoChebyshev< dim > Class Template Reference

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

Inheritance diagram for QGaussLobattoChebyshev< dim >:
Inheritance graph

Public Member Functions

 QGaussLobattoChebyshev (const unsigned int n)
 Generate a formula with n quadrature points.
 QGaussLobattoChebyshev (const unsigned int n)

Detailed Description

template<int dim>
class QGaussLobattoChebyshev< dim >

Gauss-Lobatto-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 two of the quadrature points are located at the endpoints of the quadrature interval. The nodes and weights are known analytically, and are exact for monomials up to the order \(2n-3\), 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: \(w(x) = 1/\sqrt{x(1-x)}\). For details see: M. Abramowitz & I.A. Stegun: Handbook of Mathematical Functions, par. 25.4.40

Definition at line 627 of file quadrature_lib.h.

Constructor & Destructor Documentation

◆ QGaussLobattoChebyshev() [1/2]

template<int dim>
QGaussLobattoChebyshev< dim >::QGaussLobattoChebyshev ( const unsigned int  n)

Generate a formula with n quadrature points.

Definition at line 1439 of file

◆ QGaussLobattoChebyshev() [2/2]

Definition at line 1419 of file

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