![]() |
Reference documentation for deal.II version 9.6.0
|
#include <deal.II/base/quadrature_lib.h>
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) |
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< dim >::QGaussLog | ( | const unsigned int | n, |
const bool | revert = false ) |
Generate a formula with n
quadrature points
QGaussLog< 1 >::QGaussLog | ( | const unsigned int | n, |
const bool | revert ) |
Definition at line 484 of file quadrature_lib.cc.
|
staticprivate |
Compute the points of the quadrature formula.
|
staticprivate |
Compute the weights of the quadrature formula.
Definition at line 503 of file quadrature_lib.cc.
Definition at line 636 of file quadrature_lib.cc.