Reference documentation for deal.II version 9.4.1

#include <deal.II/base/polynomials_piecewise.h>
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 int >  counter 
std::map< std::string, unsigned int >  counter_map 
std::vector< std::atomic< bool > * >  validity_pointers 
const std::type_info *  object_info 
static std::mutex  mutex 
static ::ExceptionBase &  ExcInUse (int arg1, std::string arg2, std::string arg3) 
static ::ExceptionBase &  ExcNoSubscriber (std::string arg1, std::string arg2) 
void  check_no_subscribers () const noexcept 
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 higherorder 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 subcells.
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 interfacecompatible with the Polynomials::Polynomial class, and consequently can be used as template argument for TensorProductPolynomials.
Definition at line 64 of file polynomials_piecewise.h.
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.
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.

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.
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 i
th 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.
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 i
th 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.

inline 
Degree of the polynomial. This is the degree of the underlying base polynomial.
Definition at line 235 of file polynomials_piecewise.h.

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.

virtual 
Return an estimate (in bytes) for the memory consumption of this object.
Definition at line 178 of file polynomials_piecewise.cc.

protected 
Underlying polynomial object that is scaled to a subinterval and concatenated accordingly.
Definition at line 165 of file polynomials_piecewise.h.

protected 
A variable storing the number of intervals that the unit interval is divided into.
Definition at line 171 of file polynomials_piecewise.h.

protected 
A variable storing the index of the current polynomial in the range of intervals.
Definition at line 177 of file polynomials_piecewise.h.

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.

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.

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.

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.