Reference documentation for deal.II version GIT relicensing-1312-g94296a292e 2024-07-25 16:30:01+00:00
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QSplit< dim > Class Template Reference

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

Inheritance diagram for QSplit< dim >:
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Public Member Functions

QSplit (const QSimplex< dim > &base, const Point< dim > &split_point)

Detailed Description

template<int dim>
class QSplit< dim >

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()

template<int dim>
 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:

const unsigned int order = 5;