QTrianglePolar Class Reference

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

Inheritance diagram for QTrianglePolar:

Public Member Functions
	QTrianglePolar (const Quadrature< 1 > &radial_quadrature, const Quadrature< 1 > &angular_quadrature)
	QTrianglePolar (const unsigned int &n)
Public Member Functions inherited from QSimplex< 2 >
	QSimplex (const Quadrature< dim > &quad)
Quadrature< dim >	compute_affine_transformation (const std::array< Point< dim >, dim+1 > &vertices) const
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 ()=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
std::conditional< dim==1, std::array< Quadrature< 1 >, dim >, const std::array< Quadrature< 1 >, dim > & >::type	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 (const char *identifier=nullptr) const
void	unsubscribe (const char *identifier=nullptr) const
unsigned int	n_subscriptions () 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 >
typedef Quadrature< dim-1 >	SubQuadrature
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

A quadrature that implements a polar transformation from a square to a triangle to integrate singularities in the origin of the reference simplex. The quadrature is obtained through the following polar transformation:

\[ \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} \frac{\hat x}{\sin(\theta)+\cos(\theta)} cos(\theta) \\ \frac{\hat x}{\sin(\theta)+\cos(\theta)} sin(\theta) \end{pmatrix} \qquad \theta := \frac\pi 2 \hat y \]

Author

Luca Heltai, 2017

Definition at line 671 of file quadrature_lib.h.

Constructor & Destructor Documentation

QTrianglePolar() [1/2]

QTrianglePolar::QTrianglePolar	(	const Quadrature< 1 > &	radial_quadrature,
		const Quadrature< 1 > &	angular_quadrature
	)

Construct a QTrianglePolar quadrature, with different formulas in the radial and angular directions.

Parameters

radial_quadrature	Radial quadrature
angular_quadrature	Angular quadrature

Definition at line 1242 of file quadrature_lib.cc.

QTrianglePolar() [2/2]

QTrianglePolar::QTrianglePolar

(

const unsigned int &

n

)

Call the other constructor, with QGauss<1>(n) for both radial and angular quadrature.

Parameters

n	Order of QGauss quadrature

Definition at line 1272 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