Reference documentation for deal.II version 8.4.1
Polynomials::PiecewisePolynomial< number > Class Template Reference

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

Inheritance diagram for Polynomials::PiecewisePolynomial< number >:
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## Public Member Functions

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

number value (const number x) const

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

unsigned int degree () const

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

Public Member Functions inherited from Subscriptor
Subscriptor ()

Subscriptor (const Subscriptor &)

virtual ~Subscriptor ()

Subscriptoroperator= (const Subscriptor &)

void subscribe (const char *identifier=0) const

void unsubscribe (const char *identifier=0) const

unsigned int n_subscriptions () const

void list_subscribers () const

DeclException3 (ExcInUse, int, char *, std::string &,<< "Object of class "<< arg2<< " is still used by "<< arg1<< " other objects."<< "\n\n"<< "(Additional information: "<< arg3<< ")\n\n"<< "See the entry in the Frequently Asked Questions of "<< "deal.II (linked to from http://www.dealii.org/) for "<< "a lot more information on what this error means and "<< "how to fix programs in which it happens.")

DeclException2 (ExcNoSubscriber, char *, char *,<< "No subscriber with identifier <"<< arg2<< "> subscribes to this object of class "<< arg1<< ". Consequently, it cannot be unsubscribed.")

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

## Protected Attributes

Polynomial< number > polynomial

unsigned int n_intervals

unsigned int interval

bool spans_two_intervals

## 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 the subdivided elements. This primary purpose of this class is to allow constructing FE_Q_iso_Q1 elements that put additional degrees of freedom into an equivalent of a refined mesh instead of higher order polynomials, which is useful when using mixed finite elements.

Definition at line 55 of file polynomials_piecewise.h.

## Constructor & Destructor Documentation

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 27 of file polynomials_piecewise.cc.

## Member Function Documentation

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 170 of file polynomials_piecewise.h.

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 array passed.

Note that all the derivatives evaluate to zero at the border between intervals (assuming exact arithmetics) 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 45 of file polynomials_piecewise.cc.

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 160 of file polynomials_piecewise.h.

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.

Definition at line 213 of file polynomials_piecewise.h.

## Member Data Documentation

template<typename number>
 Polynomial Polynomials::PiecewisePolynomial< number >::polynomial
protected

Underlying polynomial object that is scaled to a subinterval and concatenated accordingly.

Definition at line 118 of file polynomials_piecewise.h.

template<typename number>
 unsigned int Polynomials::PiecewisePolynomial< number >::n_intervals
protected

Stores the number of intervals that the unit interval is divided into.

Definition at line 123 of file polynomials_piecewise.h.

template<typename number>
 unsigned int Polynomials::PiecewisePolynomial< number >::interval
protected

Stores the index of the current polynomial in the range of intervals.

Definition at line 128 of file polynomials_piecewise.h.

template<typename number>
 bool Polynomials::PiecewisePolynomial< number >::spans_two_intervals
protected

Store if the polynomial spans over two adjacent intervals, i.e., the one given in subinterval and the next one.

Definition at line 134 of file polynomials_piecewise.h.

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