Reference documentation for deal.II version GIT 6bdf9a4b6c 2022-08-12 19:20:02+00:00
\(\newcommand{\dealvcentcolon}{\mathrel{\mathop{:}}}\) \(\newcommand{\dealcoloneq}{\dealvcentcolon\mathrel{\mkern-1.2mu}=}\) \(\newcommand{\jump}[1]{\left[\!\left[ #1 \right]\!\right]}\) \(\newcommand{\average}[1]{\left\{\!\left\{ #1 \right\}\!\right\}}\)
Public Types | Public Member Functions | Static Public Member Functions | Protected Attributes | Private Types | Private Member Functions | Private Attributes | Static Private Attributes | List of all members
QSimplex< dim > Class Template Reference

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

Inheritance diagram for QSimplex< dim >:

Public Types

using SubQuadrature = Quadrature< dim==0 ? 0 :dim - 1 >

Public Member Functions

 QSimplex (const Quadrature< dim > &quad)
template<int spacedim = dim>
Quadrature< spacedim > compute_affine_transformation (const std::array< Point< spacedim >, dim+1 > &vertices) const
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
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

Static Public Member Functions

static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)
static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string arg2)

Protected Attributes

std::vector< Point< dim > > quadrature_points
std::vector< doubleweights
bool is_tensor_product_flag
std::unique_ptr< std::array< Quadrature< 1 >, dim > > tensor_basis

Private Types

using map_value_type = decltype(counter_map)::value_type
using map_iterator = decltype(counter_map)::iterator

Private Member Functions

void check_no_subscribers () const noexcept

Private Attributes

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 Private Attributes

static std::mutex mutex

Detailed Description

template<int dim>
class QSimplex< dim >

Given an arbitrary quadrature formula, return one that chops the quadrature points above the hyper-plane defined by \(\sum_i x_i = 1\). In other words, it extracts those quadrature points from the base formula that satisfy \(\sum_i (\mathbf x_q)_i \le 1+10^{-12}\)."

In general the resulting quadrature is not very useful, unless the quadrature you started from has been constructed specifically to integrate over triangles or tetrahedra. This class only ensures that the resulting quadrature formula only has quadrature points in the reference simplex or on its boundary.

No transformation is applied to the weights, and the weights referring to points that live outside the reference simplex are simply discarded. Because this leads to (or may lead to) a sum of quadrature weights that do not equal the area of the simplex, the resulting quadrature formula is not useful for actually computing integrals.

The main use of this quadrature formula is not to chop tensor product quadratures. Ideally you should pass to this class a quadrature formula constructed directly using points and weights in the reference simplex, capable of integrating on triangles or tetrahedra.

For finite elements based on quadrilaterals and hexahedra, a QSimplex quadrature formula is not very useful on its own. This class is typically used in conjunction with other classes, like QSplit, to patch the reference element using several QSimplex quadrature formulas.

Such quadrature formulas are useful to integrate functions with singularities at certain points, or functions that present jumps along a co-dimension one surface inside the reference element, like in the extended finite element method (XFEM).

Definition at line 602 of file quadrature_lib.h.

Member Typedef Documentation

◆ SubQuadrature

template<int dim>
using Quadrature< dim >::SubQuadrature = Quadrature<dim == 0 ? 0 : dim - 1>

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 96 of file quadrature.h.

◆ map_value_type

using Subscriptor::map_value_type = decltype(counter_map)::value_type

The data type used in counter_map.

Definition at line 230 of file subscriptor.h.

◆ map_iterator

using Subscriptor::map_iterator = decltype(counter_map)::iterator

The iterator type used in counter_map.

Definition at line 235 of file subscriptor.h.

Constructor & Destructor Documentation

◆ QSimplex()

template<int dim>
QSimplex< dim >::QSimplex ( const Quadrature< dim > &  quad)

Construct a quadrature that only contains the points that are in the lower left reference simplex.

[in]quadThe input quadrature.

Definition at line 1205 of file

Member Function Documentation

◆ compute_affine_transformation()

template<int dim>
template<int spacedim>
template Quadrature< 3 > QSimplex< dim >::compute_affine_transformation ( const std::array< Point< spacedim >, dim+1 > &  vertices) const

Return an affine transformation of this quadrature, that can be used to integrate on the simplex identified by vertices.

Both the quadrature point locations and the weights are transformed, so that you can effectively use the resulting quadrature to integrate on the simplex.

The transformation is defined as

\[ x = v_0 + B \hat x \]

where the matrix \(B\) is given by \(B_{ij} = v[j][i]-v[0][i]\).

The weights are scaled with the absolute value of the determinant of \(B\), that is \(J \dealcoloneq |\text{det}(B)|\). If \(J\) is zero, an empty quadrature is returned. This may happen, in two dimensions, if the three vertices are aligned, or in three dimensions if the four vertices are on the same plane. The present function works also in the codimension one and codimension two case. For instance, when dim=2 and spacedim=3, we can map the quadrature points so that they live on the physical triangle embedded in the three dimensional space. In such a case, the matrix \(B\) is not square anymore.

[in]verticesThe vertices of the simplex you wish to integrate on
A quadrature object that can be used to integrate on the simplex

Definition at line 1232 of file

◆ operator==()

template<int dim>
bool Quadrature< dim >::operator== ( const Quadrature< dim > &  p) const

Test for equality of two quadratures.

Definition at line 304 of file

◆ initialize()

template<int dim>
void Quadrature< dim >::initialize ( const std::vector< Point< dim >> &  points,
const std::vector< double > &  weights 

Set the quadrature points and weights to the values provided in the arguments.

Definition at line 52 of file

◆ size()

template<int dim>
unsigned int Quadrature< dim >::size ( ) const

Number of quadrature points.

◆ point()

template<int dim>
const Point<dim>& Quadrature< dim >::point ( const unsigned int  i) const

Return the ith quadrature point.

◆ get_points()

template<int dim>
const std::vector<Point<dim> >& Quadrature< dim >::get_points ( ) const

Return a reference to the whole array of quadrature points.

◆ weight()

template<int dim>
double Quadrature< dim >::weight ( const unsigned int  i) const

Return the weight of the ith quadrature point.

◆ get_weights()

template<int dim>
const std::vector<double>& Quadrature< dim >::get_weights ( ) const

Return a reference to the whole array of weights.

◆ memory_consumption()

template<int dim>
std::size_t Quadrature< dim >::memory_consumption

Determine an estimate for the memory consumption (in bytes) of this object.

Definition at line 313 of file

◆ serialize()

template<int dim>
template<class Archive >
void Quadrature< dim >::serialize ( Archive &  ar,
const unsigned int  version 

Write or read the data of this object to or from a stream for the purpose of serialization using the BOOST serialization library.

◆ is_tensor_product()

template<int dim>
bool Quadrature< dim >::is_tensor_product ( ) const

This function returns true if the quadrature object is a tensor product of one-dimensional formulas and the quadrature points are sorted lexicographically.

◆ get_tensor_basis()

template<int dim>
std::conditional< dim==1, std::array< Quadrature< 1 >, dim >, const std::array< Quadrature< 1 >, dim > & >::type Quadrature< dim >::get_tensor_basis

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).

The actual return type of this function is
std::conditional<dim == 1,
std::array<Quadrature<1>, dim>,
const std::array<Quadrature<1>, dim> &>::type
The type is abbreviated in the online documentation to improve readability of this page.

Definition at line 325 of file

◆ subscribe()

void Subscriptor::subscribe ( std::atomic< bool > *const  validity,
const std::string &  identifier = "" 
) const

Subscribes a user of the object by storing the pointer validity. The subscriber may be identified by text supplied as identifier.

Definition at line 136 of file

◆ unsubscribe()

void Subscriptor::unsubscribe ( std::atomic< bool > *const  validity,
const std::string &  identifier = "" 
) const

Unsubscribes a user from the object.

The identifier and the validity pointer must be the same as the one supplied to subscribe().

Definition at line 156 of file

◆ n_subscriptions()

unsigned int Subscriptor::n_subscriptions ( ) const

Return the present number of subscriptions to this object. This allows to use this class for reference counted lifetime determination where the last one to unsubscribe also deletes the object.

Definition at line 300 of file subscriptor.h.

◆ list_subscribers() [1/2]

template<typename StreamType >
void Subscriptor::list_subscribers ( StreamType &  stream) const

List the subscribers to the input stream.

Definition at line 317 of file subscriptor.h.

◆ list_subscribers() [2/2]

void Subscriptor::list_subscribers ( ) const

List the subscribers to deallog.

Definition at line 204 of file

◆ check_no_subscribers()

void Subscriptor::check_no_subscribers ( ) const

Check that there are no objects subscribing to this object. If this check passes then it is safe to destroy the current object. It this check fails then this function will either abort or print an error message to deallog (by using the AssertNothrow mechanism), but will not throw an exception.

Since this function is just a consistency check it does nothing in release mode.
If this function is called when there is an uncaught exception then, rather than aborting, this function prints an error message to the standard error stream and returns.

Definition at line 53 of file

Member Data Documentation

◆ quadrature_points

template<int dim>
std::vector<Point<dim> > Quadrature< dim >::quadrature_points

List of quadrature points. To be filled by the constructors of derived classes.

Definition at line 292 of file quadrature.h.

◆ weights

template<int dim>
std::vector<double> Quadrature< dim >::weights

List of weights of the quadrature points. To be filled by the constructors of derived classes.

Definition at line 298 of file quadrature.h.

◆ is_tensor_product_flag

template<int dim>
bool Quadrature< dim >::is_tensor_product_flag

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 307 of file quadrature.h.

◆ tensor_basis

template<int dim>
std::unique_ptr<std::array<Quadrature<1>, dim> > Quadrature< dim >::tensor_basis

Stores the one-dimensional tensor basis objects in case this object can be represented by a tensor product.

Definition at line 313 of file quadrature.h.

◆ counter

std::atomic<unsigned int> Subscriptor::counter

Store the number of objects which subscribed to this object. Initially, this number is zero, and upon destruction it shall be zero again (i.e. all objects which subscribed should have unsubscribed again).

The creator (and owner) of an object is counted in the map below if HE manages to supply identification.

We use the mutable keyword in order to allow subscription to constant objects also.

This counter may be read from and written to concurrently in multithreaded code: hence we use the std::atomic class template.

Definition at line 219 of file subscriptor.h.

◆ counter_map

std::map<std::string, unsigned int> Subscriptor::counter_map

In this map, we count subscriptions for each different identification string supplied to subscribe().

Definition at line 225 of file subscriptor.h.

◆ validity_pointers

std::vector<std::atomic<bool> *> Subscriptor::validity_pointers

In this vector, we store pointers to the validity bool in the SmartPointer objects that subscribe to this class.

Definition at line 241 of file subscriptor.h.

◆ object_info

const std::type_info* Subscriptor::object_info

Pointer to the typeinfo object of this object, from which we can later deduce the class name. Since this information on the derived class is neither available in the destructor, nor in the constructor, we obtain it in between and store it here.

Definition at line 249 of file subscriptor.h.

◆ mutex

std::mutex Subscriptor::mutex

A mutex used to ensure data consistency when printing out the list of subscribers.

Definition at line 271 of file subscriptor.h.

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