Reference documentation for deal.II version GIT 75f1417c0d 20230203 16:10:02+00:00

#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 
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 
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.

privateinherited 
The data type used in counter_map.
Definition at line 230 of file subscriptor.h.

privateinherited 
The iterator type used in counter_map.
Definition at line 235 of file subscriptor.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.

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 136 of file subscriptor.cc.

inherited 
Unsubscribes a user from the object.
identifier
and the validity
pointer must be the same as the one supplied to subscribe(). Definition at line 156 of file subscriptor.cc.

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.

inlineinherited 
List the subscribers to the input stream
.
Definition at line 317 of file subscriptor.h.

inherited 
List the subscribers to deallog
.
Definition at line 204 of file subscriptor.cc.

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.
Definition at line 53 of file subscriptor.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.

mutableprivateinherited 
Store the number of objects which subscribed to this object. Initially, this number is zero, and upon destruction it shall be zero again (i.e. all objects which subscribed should have unsubscribed again).
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 219 of file subscriptor.h.

mutableprivateinherited 
In this map, we count subscriptions for each different identification string supplied to subscribe().
Definition at line 225 of file subscriptor.h.

mutableprivateinherited 
In this vector, we store pointers to the validity bool in the SmartPointer objects that subscribe to this class.
Definition at line 241 of file subscriptor.h.

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 249 of file subscriptor.h.

staticprivateinherited 
A mutex used to ensure data consistency when printing out the list of subscribers.
Definition at line 271 of file subscriptor.h.