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Reference documentation for deal.II version 8.1.0
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#include <polynomial.h>
Public Member Functions | |
Lobatto (const unsigned int p=0) | |
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Polynomial (const std::vector< double > &coefficients) | |
Polynomial (const unsigned int n) | |
Polynomial (const std::vector< Point< 1 > > &lagrange_support_points, const unsigned int evaluation_point) | |
Polynomial () | |
double | value (const doublex) const |
void | value (const doublex, std::vector< double > &values) const |
unsigned int | degree () const |
void | scale (const doublefactor) |
void | shift (const number2 offset) |
Polynomial< double > | derivative () const |
Polynomial< double > | primitive () const |
Polynomial< double > & | operator*= (const double s) |
Polynomial< double > & | operator*= (const Polynomial< double > &p) |
Polynomial< double > & | operator+= (const Polynomial< double > &p) |
Polynomial< double > & | operator-= (const Polynomial< double > &p) |
bool | operator== (const Polynomial< double > &p) const |
void | print (std::ostream &out) const |
void | serialize (Archive &ar, const unsigned int version) |
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Subscriptor () | |
Subscriptor (const Subscriptor &) | |
virtual | ~Subscriptor () |
Subscriptor & | operator= (const Subscriptor &) |
void | subscribe (const char *identifier=0) const |
void | unsubscribe (const char *identifier=0) const |
unsigned int | n_subscriptions () const |
void | list_subscribers () const |
DeclException3 (ExcInUse, int, char *, std::string &,<< "Object of class "<< arg2<< " is still used by "<< arg1<< " other objects.\n"<< "(Additional information: "<< arg3<< ")\n"<< "Note the entry in the Frequently Asked Questions of "<< "deal.II (linked to from http://www.dealii.org/) for "<< "more information on what this error means.") | |
DeclException2 (ExcNoSubscriber, char *, char *,<< "No subscriber with identifier \""<< arg2<< "\" did subscribe to this object of class "<< arg1) | |
template<class Archive > | |
void | serialize (Archive &ar, const unsigned int version) |
Static Public Member Functions | |
static std::vector< Polynomial< double > > | generate_complete_basis (const unsigned int p) |
Private Member Functions | |
std::vector< double > | compute_coefficients (const unsigned int p) |
Additional Inherited Members | |
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void | transform_into_standard_form () |
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static void | scale (std::vector< double > &coefficients, const doublefactor) |
static void | shift (std::vector< double > &coefficients, const number2 shift) |
static void | multiply (std::vector< double > &coefficients, const doublefactor) |
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std::vector< double > | coefficients |
bool | in_lagrange_product_form |
std::vector< double > | lagrange_support_points |
double | lagrange_weight |
Lobatto polynomials of arbitrary degree on [0,1]
.
These polynomials are the integrated Legendre polynomials on [0,1]. The first two polynomials are the standard linear shape functions given by and
. For
we use the definition
, where
denotes the
-th Legendre polynomial on
. The Lobatto polynomials
form a complete basis of the polynomials space of degree
.
Calling the constructor with a given index k
will generate the polynomial with index k
. But only for the index equals the degree of the polynomial. For
k==0
also a polynomial of degree 1 is generated.
These polynomials are used for the construction of the shape functions of Nédélec elements of arbitrary order.
Definition at line 464 of file polynomial.h.
Polynomials::Lobatto::Lobatto | ( | const unsigned int | p = 0 | ) |
Constructor for polynomial of degree p
. There is an exception for p==0
, see the general documentation.
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static |
Return the polynomials with index 0
up to degree
. There is an exception for p==0
, see the general documentation.
Compute coefficients recursively.