![]() |
Reference documentation for deal.II version 9.4.1
|
#include <deal.II/base/quadrature_lib.h>
Public Types | |
using | SubQuadrature = Quadrature< dim==0 ? 0 :dim - 1 > |
Public Member Functions | |
QGaussOneOverR (const unsigned int n, const Point< dim > &singularity, const bool factor_out_singular_weight=false) | |
QGaussOneOverR (const unsigned int n, const unsigned int vertex_index, const bool factor_out_singular_weight=false) | |
QGaussOneOverR (const unsigned int n, const Point< 2 > &singularity, const bool factor_out_singularity) | |
QGaussOneOverR (const unsigned int n, const unsigned int vertex_index, const bool factor_out_singularity) | |
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 |
Protected Attributes | |
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 |
Private Member Functions | |
unsigned int | quad_size (const Point< 2 > &singularity, const unsigned int n) |
Static Private Member Functions | |
static unsigned int | quad_size (const Point< dim > &singularity, const unsigned int n) |
Subscriptor functionality | |
Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class. | |
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 |
void | check_no_subscribers () const noexcept |
using | map_value_type = decltype(counter_map)::value_type |
using | map_iterator = decltype(counter_map)::iterator |
std::atomic< unsigned int > | counter |
std::map< std::string, unsigned int > | counter_map |
std::vector< std::atomic< bool > * > | validity_pointers |
const std::type_info * | object_info |
static std::mutex | mutex |
static ::ExceptionBase & | ExcInUse (int arg1, std::string arg2, std::string arg3) |
static ::ExceptionBase & | ExcNoSubscriber (std::string arg1, std::string arg2) |
A class for Gauss quadrature with 1/R weighting function. This formula can be used to integrate 1/R \ f(x) on the reference element [0,1]^2, where f is a smooth function without singularities, and R is the distance from the point x to the vertex \xi, given at construction time by specifying its index. Notice that this distance is evaluated in the reference element.
This quadrature formula is obtained from two QGauss quadrature formulas, upon transforming them into polar coordinate system centered at the singularity, and then again into another reference element. This allows for the singularity to be cancelled by part of the Jacobian of the transformation, which contains R. In practice the reference element is transformed into a triangle by collapsing one of the sides adjacent to the singularity. The Jacobian of this transformation contains R, which is removed before scaling the original quadrature, and this process is repeated for the next half element.
Upon construction it is possible to specify whether we want the singularity removed, or not. In other words, this quadrature can be used to integrate g(x) = 1/R\ f(x), or simply f(x), with the 1/R factor already included in the quadrature weights.
Definition at line 305 of file quadrature_lib.h.
|
inherited |
Define an alias for a quadrature that acts on an object of one dimension less. For cells, this would then be a face quadrature. A sub quadrature of a 0-dimensional quadrature is defined as still being 0-dimensional.
Definition at line 94 of file quadrature.h.
QGaussOneOverR< dim >::QGaussOneOverR | ( | const unsigned int | n, |
const Point< dim > & | singularity, | ||
const bool | factor_out_singular_weight = false |
||
) |
This constructor takes three arguments: the order of the Gauss formula, the point of the reference element in which the singularity is located, and whether we include the weighting singular function inside the quadrature, or we leave it in the user function to be integrated.
Traditionally, quadrature formulas include their weighting function, and the last argument is set to false by default. There are cases, however, where this is undesirable (for example when you only know that your singularity has the same order of 1/R, but cannot be written exactly in this way).
In other words, you can use this function in either of the following way, obtaining the same result:
QGaussOneOverR< dim >::QGaussOneOverR | ( | const unsigned int | n, |
const unsigned int | vertex_index, | ||
const bool | factor_out_singular_weight = false |
||
) |
The constructor takes three arguments: the order of the Gauss formula, the index of the vertex where the singularity is located, and whether we include the weighting singular function inside the quadrature, or we leave it in the user function to be integrated. Notice that this is a specialized version of the previous constructor which works only for the vertices of the quadrilateral.
Traditionally, quadrature formulas include their weighting function, and the last argument is set to false by default. There are cases, however, where this is undesirable (for example when you only know that your singularity has the same order of 1/R, but cannot be written exactly in this way).
In other words, you can use this function in either of the following way, obtaining the same result:
QGaussOneOverR< 2 >::QGaussOneOverR | ( | const unsigned int | n, |
const Point< 2 > & | singularity, | ||
const bool | factor_out_singularity | ||
) |
Definition at line 637 of file quadrature_lib.cc.
QGaussOneOverR< 2 >::QGaussOneOverR | ( | const unsigned int | n, |
const unsigned int | vertex_index, | ||
const bool | factor_out_singularity | ||
) |
Definition at line 686 of file quadrature_lib.cc.
|
staticprivate |
Given a quadrature point and a degree n, this function returns the size of the singular quadrature rule, considering whether the point is inside the cell, on an edge of the cell, or on a corner of the cell.
|
private |
Definition at line 616 of file quadrature_lib.cc.
|
inherited |
Test for equality of two quadratures.
Definition at line 304 of file quadrature.cc.
|
inherited |
Set the quadrature points and weights to the values provided in the arguments.
Definition at line 52 of file quadrature.cc.
|
inherited |
Number of quadrature points.
|
inherited |
Return the i
th quadrature point.
|
inherited |
Return a reference to the whole array of quadrature points.
|
inherited |
Return the weight of the i
th quadrature point.
|
inherited |
Return a reference to the whole array of weights.
|
inherited |
Determine an estimate for the memory consumption (in bytes) of this object.
Definition at line 313 of file quadrature.cc.
|
inherited |
Write or read the data of this object to or from a stream for the purpose of serialization using the BOOST serialization library.
|
inherited |
This function returns true if the quadrature object is a tensor product of one-dimensional formulas and the quadrature points are sorted lexicographically.
|
inherited |
In case the quadrature formula is a tensor product, this function returns the dim
one-dimensional basis objects. Otherwise, calling this function is not allowed.
For dim
equal to one, we can not return the std::array as a const reference and have to return it by value. In this case, the array will always contain a single element (this
).
Definition at line 325 of file quadrature.cc.
|
protectedinherited |
List of quadrature points. To be filled by the constructors of derived classes.
Definition at line 290 of file quadrature.h.
|
protectedinherited |
List of weights of the quadrature points. To be filled by the constructors of derived classes.
Definition at line 296 of file quadrature.h.
|
protectedinherited |
Indicates if this object represents quadrature formula that is a tensor product of one-dimensional formulas. This flag is set if dim==1 or the constructors taking a Quadrature<1> (and possibly a Quadrature<dim-1> object) is called. This implies that the quadrature points are sorted lexicographically.
Definition at line 305 of file quadrature.h.
|
protectedinherited |
Stores the one-dimensional tensor basis objects in case this object can be represented by a tensor product.
Definition at line 311 of file quadrature.h.