Reference documentation for deal.II version 9.4.0
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)

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

## 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

## 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

using map_value_type = decltype(counter_map)::value_type

using map_iterator = decltype(counter_map)::iterator

std::atomic< unsigned intcounter

std::map< std::string, unsigned intcounter_map

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

const std::type_info * object_info

static std::mutex mutex

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

static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string arg2)

void check_no_subscribers () const noexcept

## 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 64 of file polynomials_piecewise.h.

## ◆ 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 27 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 45 of file polynomials_piecewise.cc.

## ◆ 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 246 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 70 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 82 of file polynomials_piecewise.cc.

## ◆ degree()

template<typename number >
 unsigned int Polynomials::PiecewisePolynomial< number >::degree
inline

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

Definition at line 235 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 302 of file polynomials_piecewise.h.

## ◆ memory_consumption()

template<typename number >
 std::size_t Polynomials::PiecewisePolynomial< number >::memory_consumption
virtual

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

Definition at line 178 of file polynomials_piecewise.cc.

## ◆ polynomial

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

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

Definition at line 165 of file polynomials_piecewise.h.

## ◆ n_intervals

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

A variable storing the number of intervals that the unit interval is divided into.

Definition at line 171 of file polynomials_piecewise.h.

## ◆ interval

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

A variable storing the index of the current polynomial in the range of intervals.

Definition at line 177 of file polynomials_piecewise.h.

## ◆ spans_two_intervals

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 183 of file polynomials_piecewise.h.

## ◆ points

template<typename number >
 std::vector Polynomials::PiecewisePolynomial< number >::points
protected

Points bounding the subintervals in the case that piecewise linear polynomial on varying subintervals is requested.

Definition at line 189 of file polynomials_piecewise.h.

## ◆ one_over_lengths

template<typename number >
 std::vector Polynomials::PiecewisePolynomial< number >::one_over_lengths
protected

Precomputed inverses of the lengths of the subintervals, i.e., one_over_lengths[i] = 1.0 / (points[i + 1] - points[i].

Definition at line 195 of file polynomials_piecewise.h.

## ◆ index

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

A variable storing the index of the current polynomial in the case that piecewise linear polynomial on varying subintervals is requested.

Definition at line 201 of file polynomials_piecewise.h.

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