Reference documentation for deal.II version Git 1a03d59 2018-10-17 14:28:31 +0200
Public Member Functions | List of all members
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 () override=default
Quadratureoperator= (const Quadrature< dim > &)
Quadratureoperator= (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 ()
Subscriptoroperator= (const Subscriptor &)
Subscriptoroperator= (Subscriptor &&) noexcept
void subscribe (const char *identifier=nullptr) const
void unsubscribe (const char *identifier=nullptr) 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

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:

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

Luca Heltai, 2017

Definition at line 670 of file quadrature_lib.h.

Constructor & Destructor Documentation

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.

radial_quadratureRadial quadrature
angular_quadratureAngular quadrature

Definition at line 1248 of file

QTrianglePolar::QTrianglePolar ( const unsigned int  n)

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

nOrder of QGauss quadrature

Definition at line 1278 of file

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