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

Inheritance diagram for Polynomials::PiecewisePolynomial< number >:

Public Member Functions
	PiecewisePolynomial (const Polynomial< number > &coefficients_on_interval, const unsigned int n_intervals, const unsigned int interval, const bool spans_next_interval)

	PiecewisePolynomial (const std::vector< Point< 1, number > > &points, const unsigned int index)

number	value (const number x) const

void	value (const number x, std::vector< number > &values) const

void	value (const number x, const unsigned int n_derivatives, number *values) const

unsigned int	degree () const

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

virtual std::size_t	memory_consumption () 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 ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

static ::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string arg2)

Protected Attributes
Polynomial< number >	polynomial

unsigned int	n_intervals

unsigned int	interval

bool	spans_two_intervals

std::vector< number >	points

std::vector< number >	one_over_lengths

unsigned int	index

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<typename number>
class Polynomials::PiecewisePolynomial< number >

Definition of piecewise 1d polynomials for the unit interval. This space allows the description of interpolating polynomials on parts of the unit interval, similarly to the definition of finite element basis functions on subdivided elements. The primary purpose of this class is to allow constructing the shape functions of the FE_Q_iso_Q1 class that has a number of interpolation points in each coordinate direction, but instead of using them for higher-order polynomials just chooses piecewise linear shape functions – in effect, it is a \(Q_1\) element defined on a subdivision of the reference cell, and replicated on each of these sub-cells.

This class is not derived from the ScalarPolynomialsBase base class because it is not actually a polynomial – it is a piecewise polynomial. However, it is interface-compatible with the Polynomials::Polynomial class, and consequently can be used as template argument for TensorProductPolynomials.

Definition at line 63 of file polynomials_piecewise.h.

Member Typedef Documentation

◆ map_value_type

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

privateinherited

The data type used in counter_map.

Definition at line 229 of file subscriptor.h.

◆ map_iterator

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

privateinherited

The iterator type used in counter_map.

Definition at line 234 of file subscriptor.h.

Constructor & Destructor Documentation

◆ PiecewisePolynomial() [1/2]

template<typename number >

Polynomials::PiecewisePolynomial< number >::PiecewisePolynomial	(	const Polynomial< number > &	coefficients_on_interval,
		const unsigned int	n_intervals,
		const unsigned int	interval,
		const bool	spans_next_interval )

Constructor for Lagrange polynomial on an interval that is a subset of the unit interval. It uses a polynomial description that is scaled to the size of the subinterval compared to the unit interval, the total number of intervals (subdivisions), the current index of the interval as well as if the polynomial spans onto the next interval (e.g., if it lives on two neighboring intervals).

If the number of intervals is one, the piecewise polynomial behaves exactly like a usual polynomial.

Definition at line 26 of file polynomials_piecewise.cc.

◆ PiecewisePolynomial() [2/2]

template<typename number >

Polynomials::PiecewisePolynomial< number >::PiecewisePolynomial	(	const std::vector< Point< 1, number > > &	points,
		const unsigned int	index )

Constructor for linear Lagrange polynomial on an interval that is a subset of the unit interval. It uses a polynomial description that is scaled to the size of the subinterval compared to the unit interval. The subintervals are bounded by the adjacent points in points.

Definition at line 44 of file polynomials_piecewise.cc.

Member Function Documentation

◆ value() [1/3]

template<typename number >

number Polynomials::PiecewisePolynomial< number >::value ( const number x ) const

inline

Return the value of this polynomial at the given point, evaluating the underlying polynomial. The polynomial evaluates to zero when outside of the given interval (and possible the next one to the right when it spans over that range).

Definition at line 245 of file polynomials_piecewise.h.

◆ value() [2/3]

template<typename number >

void Polynomials::PiecewisePolynomial< number >::value	(	const number	x,
		std::vector< number > &	values ) const

Return the values and the derivatives of the Polynomial at point x. values[i], i=0,...,values.size()-1 includes the ith derivative. The number of derivatives to be computed is thus determined by the size of the vector passed.

Note that all the derivatives evaluate to zero at the border between intervals (assuming exact arithmetic) in the interior of the unit interval, as there is no unique gradient value in that case for a piecewise polynomial. This is not always desired (e.g., when evaluating jumps of gradients on the element boundary), but it is the user's responsibility to avoid evaluation at these points when it does not make sense.

Definition at line 69 of file polynomials_piecewise.cc.

◆ value() [3/3]

template<typename number >

void Polynomials::PiecewisePolynomial< number >::value	(	const number	x,
		const unsigned int	n_derivatives,
		number *	values ) const

Return the values and the derivatives of the Polynomial at point x. values[i], i=0,...,n_derivatives includes the ith derivative.The number of derivatives to be computed is determined by n_derivatives and values has to provide sufficient space for n_derivatives + 1 values.

Note that all the derivatives evaluate to zero at the border between intervals (assuming exact arithmetic) in the interior of the unit interval, as there is no unique gradient value in that case for a piecewise polynomial. This is not always desired (e.g., when evaluating jumps of gradients on the element boundary), but it is the user's responsibility to avoid evaluation at these points when it does not make sense.

Definition at line 81 of file polynomials_piecewise.cc.

◆ degree()

template<typename number >

unsigned int Polynomials::PiecewisePolynomial< number >::degree ( ) const

inline

Degree of the polynomial. This is the degree of the underlying base polynomial.

Definition at line 234 of file polynomials_piecewise.h.

◆ serialize()

template<typename number >

template<class Archive >

void Polynomials::PiecewisePolynomial< number >::serialize	(	Archive &	ar,
		const unsigned int	version )

inline

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

Definition at line 301 of file polynomials_piecewise.h.

◆ memory_consumption()

template<typename number >

std::size_t Polynomials::PiecewisePolynomial< number >::memory_consumption ( ) const

virtual

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

Definition at line 177 of file polynomials_piecewise.cc.

◆ subscribe()

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

inherited

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

Definition at line 135 of file subscriptor.cc.

◆ unsubscribe()

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

inherited

Unsubscribes a user from the object.

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

Definition at line 155 of file subscriptor.cc.

◆ n_subscriptions()

unsigned int Subscriptor::n_subscriptions ( ) const

inlineinherited

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

inlineinherited

List the subscribers to the input stream.

Definition at line 317 of file subscriptor.h.

◆ list_subscribers() [2/2]

void Subscriptor::list_subscribers ( ) const

inherited

List the subscribers to deallog.

Definition at line 203 of file subscriptor.cc.

◆ check_no_subscribers()

void Subscriptor::check_no_subscribers ( ) const

privatenoexceptinherited

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.

Note: 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.

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 218 of file subscriptor.h.

◆ counter_map

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

mutableprivateinherited

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

Definition at line 224 of file subscriptor.h.

◆ validity_pointers

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

mutableprivateinherited

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

Definition at line 240 of file subscriptor.h.

◆ object_info

const std::type_info* Subscriptor::object_info

mutableprivateinherited

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 248 of file subscriptor.h.

◆ mutex

std::mutex Subscriptor::mutex

staticprivateinherited

A mutex used to ensure data consistency when accessing the mutable members of this class. This lock is used in the subscribe() and unsubscribe() functions, as well as in list_subscribers().

Definition at line 271 of file subscriptor.h.

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

include/deal.II/base/polynomials_piecewise.h
source/base/polynomials_piecewise.cc

Public Member Functions

Static Public Member Functions

Protected Attributes

Private Types

Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

Member Typedef Documentation

◆ map_value_type

◆ map_iterator

Constructor & Destructor Documentation

◆ PiecewisePolynomial() [1/2]

◆ PiecewisePolynomial() [2/2]

Member Function Documentation

◆ value() [1/3]

◆ value() [2/3]

◆ value() [3/3]

◆ degree()

◆ serialize()

◆ memory_consumption()

◆ subscribe()

◆ unsubscribe()

◆ n_subscriptions()

◆ list_subscribers() [1/2]

◆ list_subscribers() [2/2]

◆ check_no_subscribers()

Member Data Documentation

◆ polynomial

◆ n_intervals

◆ interval

◆ spans_two_intervals

◆ points

◆ one_over_lengths

◆ index

◆ counter

◆ counter_map

◆ validity_pointers

◆ object_info

◆ mutex