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Reference documentation for deal.II version 9.6.0
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#include <deal.II/base/quadrature_lib.h>
Public Types | |
enum | EndPoint { left , right } |
Public Member Functions | |
QGaussRadauChebyshev (const unsigned int n, const EndPoint end_point=QGaussRadauChebyshev::EndPoint::left) | |
Generate a formula with n quadrature points. | |
QGaussRadauChebyshev (QGaussRadauChebyshev< dim > &&) noexcept=default | |
QGaussRadauChebyshev (const unsigned int n, const EndPoint end_point) | |
Private Attributes | |
const EndPoint | end_point |
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.
enum QGaussRadauChebyshev::EndPoint |
EndPoint is used to specify which of the two endpoints of the unit interval is used also as quadrature point.
Enumerator | |
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left | Left end point. |
right | Right end point. |
Definition at line 588 of file quadrature_lib.h.
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.
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defaultnoexcept |
Move constructor.
QGaussRadauChebyshev< 1 >::QGaussRadauChebyshev | ( | const unsigned int | n, |
const EndPoint | end_point ) |
Definition at line 1346 of file quadrature_lib.cc.
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private |
Definition at line 610 of file quadrature_lib.h.