Reference documentation for deal.II version Git a5ed68a04a 20190922 06:50:58 0600

#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)  
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) 
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 (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 
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 
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) 
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.
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.

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 193 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 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 44 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 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 56 of file polynomials_piecewise.cc.

inline 
Degree of the polynomial. This is the degree of the underlying base polynomial.
Definition at line 184 of file polynomials_piecewise.h.

inline 
Write or read the data of this object to or from a stream for the purpose of serialization.
Definition at line 235 of file polynomials_piecewise.h.

protected 
Underlying polynomial object that is scaled to a subinterval and concatenated accordingly.
Definition at line 140 of file polynomials_piecewise.h.

protected 
A variable storing the number of intervals that the unit interval is divided into.
Definition at line 146 of file polynomials_piecewise.h.

protected 
A variable storing the index of the current polynomial in the range of intervals.
Definition at line 152 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 158 of file polynomials_piecewise.h.