#include <deal.II/base/quadrature_lib.h>
Public Member Functions | |
QGaussOneOverR (const unsigned int n, const Point< dim > &singularity, const bool factor_out_singular_weight=false) | |
QGaussOneOverR (const unsigned int n, const unsigned int vertex_index, const bool factor_out_singular_weight=false) | |
QGaussOneOverR (const unsigned int n, const Point< 2 > &singularity, const bool factor_out_singularity) | |
QGaussOneOverR (const unsigned int n, const unsigned int vertex_index, const bool factor_out_singularity) | |
Private Member Functions | |
unsigned int | quad_size (const Point< 2 > &singularity, const unsigned int n) |
Static Private Member Functions | |
static unsigned int | quad_size (const Point< dim > &singularity, const unsigned int n) |
A class for Gauss quadrature with
This quadrature formula is obtained from two QGauss quadrature formulas, upon transforming them into polar coordinate system centered at the singularity, and then again into another reference element. This allows for the singularity to be cancelled by part of the Jacobian of the transformation, which contains
Upon construction it is possible to specify whether we want the singularity removed, or not. In other words, this quadrature can be used to integrate
Definition at line 356 of file quadrature_lib.h.
QGaussOneOverR< dim >::QGaussOneOverR | ( | const unsigned int | n, |
const Point< dim > & | singularity, | ||
const bool | factor_out_singular_weight = false ) |
This constructor takes three arguments: the order of the Gauss formula, the point of the reference element in which the singularity is located, and whether we include the weighting singular function inside the quadrature, or we leave it in the user function to be integrated.
Traditionally, quadrature formulas include their weighting function, and the last argument is set to false by default. There are cases, however, where this is undesirable (for example when you only know that your singularity has the same order of 1/R, but cannot be written exactly in this way).
In other words, you can use this function in either of the following way, obtaining the same result:
QGaussOneOverR< dim >::QGaussOneOverR | ( | const unsigned int | n, |
const unsigned int | vertex_index, | ||
const bool | factor_out_singular_weight = false ) |
The constructor takes three arguments: the order of the Gauss formula, the index of the vertex where the singularity is located, and whether we include the weighting singular function inside the quadrature, or we leave it in the user function to be integrated. Notice that this is a specialized version of the previous constructor which works only for the vertices of the quadrilateral.
Traditionally, quadrature formulas include their weighting function, and the last argument is set to false by default. There are cases, however, where this is undesirable (for example when you only know that your singularity has the same order of 1/R, but cannot be written exactly in this way).
In other words, you can use this function in either of the following way, obtaining the same result:
QGaussOneOverR< 2 >::QGaussOneOverR | ( | const unsigned int | n, |
const Point< 2 > & | singularity, | ||
const bool | factor_out_singularity ) |
Definition at line 867 of file quadrature_lib.cc.
QGaussOneOverR< 2 >::QGaussOneOverR | ( | const unsigned int | n, |
const unsigned int | vertex_index, | ||
const bool | factor_out_singularity ) |
Definition at line 916 of file quadrature_lib.cc.
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staticprivate |
Given a quadrature point and a degree n, this function returns the size of the singular quadrature rule, considering whether the point is inside the cell, on an edge of the cell, or on a corner of the cell.
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private |
Definition at line 848 of file quadrature_lib.cc.