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Reference documentation for deal.II version 9.0.0
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Reference documentation for deal.II version 9.0.0
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#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 (const char *identifier=nullptr) const |
| void | unsubscribe (const char *identifier=nullptr) const |
| unsigned int | n_subscriptions () 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 27 of file polynomials_piecewise.cc.
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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 189 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 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 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.
| 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 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 57 of file polynomials_piecewise.cc.
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Degree of the polynomial. This is the degree of the underlying base polynomial.
Definition at line 179 of file polynomials_piecewise.h.
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Write or read the data of this object to or from a stream for the purpose of serialization.
Definition at line 232 of file polynomials_piecewise.h.
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Underlying polynomial object that is scaled to a subinterval and concatenated accordingly.
Definition at line 137 of file polynomials_piecewise.h.
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A variable storing the number of intervals that the unit interval is divided into.
Definition at line 142 of file polynomials_piecewise.h.
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A variable storing the index of the current polynomial in the range of intervals.
Definition at line 147 of file polynomials_piecewise.h.
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Store if the polynomial spans over two adjacent intervals, i.e., the one given in subinterval and the next one.
Definition at line 153 of file polynomials_piecewise.h.
1.8.14