Reference documentation for deal.II version GIT relicensing1062gc06da148b8 20240715 19:20:02+00:00

#include <deal.II/base/quadrature_lib.h>
Public Member Functions  
QSplit (const QSimplex< dim > &base, const Point< dim > &split_point)  
A quadrature to use when the cell should be split into subregions to integrate using one or more base quadratures.
Definition at line 838 of file quadrature_lib.h.
QSplit< dim >::QSplit  (  const QSimplex< dim > &  base, 
const Point< dim > &  split_point  
) 
Construct a quadrature formula by splitting the reference hyper cube into the minimum number of simplices that have vertex zero coinciding with split_point
, and patch together affine transformations of the base
quadrature. The point split_point
should be in the reference element, and an exception is thrown if this is not the case.
In two dimensions, the resulting quadrature formula will be composed of two, three, or four triangular quadrature formulas if split_point
coincides with one of the vertices, if it lies on one of the edges, or if it is internal to the reference element respectively.
The same is true for the three dimensional case, with six, eight, ten, or twelve tetrahedral quadrature formulas if split_point
coincides with one of the vertices, if it lies on one of the edges, on one of the faces, or if it is internal to the reference element respectively.
The resulting quadrature can be used, for example, to integrate functions with integrable singularities at the split point, provided that you select as base quadrature one that can integrate singular points on vertex zero of the reference simplex.
An example usage in dimension two is given by:
The resulting quadrature will look like the following:
base  Base QSimplex quadrature to use 
split_point  Where to split the hyper cube 
Definition at line 1605 of file quadrature_lib.cc.