QSplit< dim > Class Template Reference

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

Inheritance diagram for QSplit< dim >:

Public Member Functions
	QSplit (const QSimplex< dim > &base, const Point< dim > &split_point)
Public Member Functions inherited from Quadrature< dim >
	Quadrature (const unsigned int n_quadrature_points=0)
	Quadrature (const SubQuadrature &, const Quadrature< 1 > &)
	Quadrature (const Quadrature< dim !=1 ? 1 :0 > &quadrature_1d)
	Quadrature (const Quadrature< dim > &q)
	Quadrature (Quadrature< dim > &&) noexcept=default
	Quadrature (const std::vector< Point< dim >> &points, const std::vector< double > &weights)
	Quadrature (const std::vector< Point< dim >> &points)
	Quadrature (const Point< dim > &point)
virtual	~Quadrature () override=default
Quadrature &	operator= (const Quadrature< dim > &)
Quadrature &	operator= (Quadrature< dim > &&)=default
bool	operator== (const Quadrature< dim > &p) const
void	initialize (const std::vector< Point< dim >> &points, const std::vector< double > &weights)
unsigned int	size () const
const Point< dim > &	point (const unsigned int i) const
const std::vector< Point< dim > > &	get_points () const
double	weight (const unsigned int i) const
const std::vector< double > &	get_weights () const
std::size_t	memory_consumption () const
template<class Archive >
void	serialize (Archive &ar, const unsigned int version)
bool	is_tensor_product () const
const std::array< Quadrature< 1 >, dim > &	get_tensor_basis () const
Public Member Functions inherited from Subscriptor
	Subscriptor ()
	Subscriptor (const Subscriptor &)
	Subscriptor (Subscriptor &&) noexcept
virtual	~Subscriptor ()
Subscriptor &	operator= (const Subscriptor &)
Subscriptor &	operator= (Subscriptor &&) noexcept
void	subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
void	unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
unsigned int	n_subscriptions () const
template<typename StreamType >
void	list_subscribers (StreamType &stream) const
void	list_subscribers () const
template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

Additional Inherited Members
Public Types inherited from Quadrature< dim >
using	SubQuadrature = Quadrature< dim - 1 >
Static Public Member Functions inherited from Subscriptor
static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)
static ::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string arg2)
Protected Attributes inherited from Quadrature< dim >
std::vector< Point< dim > >	quadrature_points
std::vector< double >	weights
bool	is_tensor_product_flag
std::unique_ptr< std::array< Quadrature< 1 >, dim > >	tensor_basis

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.

Author

Luca Heltai, 2017.

Definition at line 764 of file quadrature_lib.h.

Constructor & Destructor Documentation

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;
QSplit<2> quad(QTrianglePolar(order), Point<2>(.3,.4));

The resulting quadrature will look like the following:

Parameters

base	Base QSimplex quadrature to use
split_point	Where to split the hyper cube

Definition at line 1319 of file quadrature_lib.cc.

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The documentation for this class was generated from the following files:

• deal.II/base/quadrature_lib.h
• source/base/quadrature_lib.cc