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Reference documentation for deal.II version 9.1.0-pre
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Reference documentation for deal.II version 9.1.0-pre
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#include <deal.II/base/quadrature.h>
Public Types | |
| using | SubQuadrature = Quadrature< dim-1 > |
Public Member Functions | |
| 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 |
| 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 |
| template<typename StreamType > | |
| void | list_subscribers (StreamType &stream) const |
| void | list_subscribers () const |
| template<class Archive > | |
| void | serialize (Archive &ar, const unsigned int version) |
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 |
Additional Inherited Members | |
| 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) |
Base class for quadrature formulae in arbitrary dimensions. This class stores quadrature points and weights on the unit line [0,1], unit square [0,1]x[0,1], etc.
There are a number of derived classes, denoting concrete integration formulae. Their names are prefixed by Q. Refer to the list of derived classes for more details.
The schemes for higher dimensions are typically tensor products of the one- dimensional formulae, but refer to the section on implementation detail below.
In order to allow for dimension independent programming, a quadrature formula of dimension zero exists. Since an integral over zero dimensions is the evaluation at a single point, any constructor of such a formula initializes to a single quadrature point with weight one. Access to the weight is possible, while access to the quadrature point is not permitted, since a Point of dimension zero contains no information. The main purpose of these formulae is their use in QProjector, which will create a useful formula of dimension one out of them.
For each quadrature formula we denote by m, the maximal degree of polynomials integrated exactly. This number is given in the documentation of each formula. The order of the integration error is m+1, that is, the error is the size of the cell to the m+1 by the Bramble- Hilbert Lemma. The number m is to be found in the documentation of each concrete formula. For the optimal formulae QGauss we have \(m = 2N-1\), where N is the constructor parameter to QGauss. The tensor product formulae are exact on tensor product polynomials of degree m in each space direction, but they are still only of m+1st order.
Most integration formulae in more than one space dimension are tensor products of quadrature formulae in one space dimension, or more generally the tensor product of a formula in (dim-1) dimensions and one in one dimension. There is a special constructor to generate a quadrature formula from two others. For example, the QGauss<dim> formulae include Ndim quadrature points in dim dimensions, where N is the constructor parameter of QGauss.
Definition at line 85 of file quadrature.h.
| using Quadrature< dim >::SubQuadrature = Quadrature<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.
Definition at line 92 of file quadrature.h.
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explicit |
Constructor.
This constructor is marked as explicit to avoid involuntary accidents like in hp::QCollection<dim> q_collection(3) where hp::QCollection<dim> q_collection(QGauss<dim>(3)) was meant.
Definition at line 40 of file quadrature.cc.
| Quadrature< dim >::Quadrature | ( | const SubQuadrature< dim > & | q1, |
| const Quadrature< 1 > & | q2 | ||
| ) |
Build this quadrature formula as the tensor product of a formula in a dimension one less than the present and a formula in one dimension. This constructor assumes (and tests) that constant functions are integrated exactly, i.e. the sum of the quadrature weights is one.
SubQuadrature<dim>::type expands to Quadrature<dim-1>.
Definition at line 119 of file quadrature.cc.
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explicit |
Build this quadrature formula as the dim-fold tensor product of a formula in one dimension.
Assuming that the points in the one-dimensional rule are in ascending order, the points of the resulting rule are ordered lexicographically with x running fastest.
In order to avoid a conflict with the copy constructor in 1d, we let the argument be a 0d quadrature formula for dim==1, and a 1d quadrature formula for all other space dimensions.
This constructor does not require that constant functions are integrated exactly. Therefore, it is appropriate if the one-dimensional formula is defined with respect to a weighting function.
Definition at line 222 of file quadrature.cc.
| Quadrature< dim >::Quadrature | ( | const Quadrature< dim > & | q | ) |
Copy constructor.
Definition at line 260 of file quadrature.cc.
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defaultnoexcept |
Move constructor. Construct a new quadrature object by transferring the internal data of another quadrature object.
| Quadrature< dim >::Quadrature | ( | const std::vector< Point< dim >> & | points, |
| const std::vector< double > & | weights | ||
| ) |
Construct a quadrature formula from given vectors of quadrature points (which should really be in the unit cell) and the corresponding weights. You will want to have the weights sum up to one, but this is not checked.
Definition at line 61 of file quadrature.cc.
| Quadrature< dim >::Quadrature | ( | const std::vector< Point< dim >> & | points | ) |
Construct a dummy quadrature formula from a list of points, with weights set to infinity. The resulting object is therefore not meant to actually perform integrations, but rather to be used with FEValues objects in order to find the position of some points (the quadrature points in this object) on the transformed cell in real space.
Definition at line 74 of file quadrature.cc.
| Quadrature< dim >::Quadrature | ( | const Point< dim > & | point | ) |
Constructor for a one-point quadrature. Sets the weight of this point to one.
Definition at line 86 of file quadrature.cc.
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overridevirtualdefault |
Virtual destructor.
| Quadrature< dim > & Quadrature< dim >::operator= | ( | const Quadrature< dim > & | q | ) |
Assignment operator. Copies contents of weights and quadrature_points as well as size.
Definition at line 275 of file quadrature.cc.
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default |
Move assignment operator. Moves all data from another quadrature object to this object.
| bool Quadrature< dim >::operator== | ( | const Quadrature< dim > & | p | ) | const |
Test for equality of two quadratures.
Definition at line 295 of file quadrature.cc.
| 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 50 of file quadrature.cc.
| unsigned int Quadrature< dim >::size | ( | ) | const |
Number of quadrature points.
| const Point<dim>& Quadrature< dim >::point | ( | const unsigned int | i | ) | const |
Return the ith quadrature point.
| const std::vector<Point<dim> >& Quadrature< dim >::get_points | ( | ) | const |
Return a reference to the whole array of quadrature points.
| double Quadrature< dim >::weight | ( | const unsigned int | i | ) | const |
Return the weight of the ith quadrature point.
| const std::vector<double>& Quadrature< dim >::get_weights | ( | ) | const |
Return a reference to the whole array of weights.
| std::size_t Quadrature< dim >::memory_consumption | ( | ) | const |
Determine an estimate for the memory consumption (in bytes) of this object.
Definition at line 304 of file quadrature.cc.
| 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.
| 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.
| std::conditional< dim==1, std::array< Quadrature< 1 >, dim >, const std::array< Quadrature< 1 >, dim > & >::type Quadrature< dim >::get_tensor_basis | ( | ) | const |
In case the quadrature formula is a tensor product, this function returns the one-dimensional basis objects. Otherwise, calling this function is not allowed.
Definition at line 316 of file quadrature.cc.
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protected |
List of quadrature points. To be filled by the constructors of derived classes.
Definition at line 267 of file quadrature.h.
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protected |
List of weights of the quadrature points. To be filled by the constructors of derived classes.
Definition at line 273 of file quadrature.h.
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protected |
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 282 of file quadrature.h.
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protected |
Stores the one-dimensional tensor basis objects in case this object can be represented by a tensor product.
Definition at line 288 of file quadrature.h.
1.8.11
