Reference documentation for deal.II version Git 053e5b2 2017-07-21 22:33:36 -0600
Public Member Functions | Static Public Member Functions | Static Private Member Functions | List of all members
IntegratedLegendreSZ Class Reference

#include <deal.II/base/polynomials_integrated_legendre_sz.h>

Inheritance diagram for IntegratedLegendreSZ:
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Public Member Functions

 IntegratedLegendreSZ (const unsigned int p)
 
- Public Member Functions inherited from Polynomials::Polynomial< double >
 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
 
void value (const doublex, const unsigned int n_derivatives, 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)
 
- Public Member Functions inherited from Subscriptor
 Subscriptor ()
 
 Subscriptor (const Subscriptor &)
 
 Subscriptor (Subscriptor &&)
 
virtual ~Subscriptor ()
 
Subscriptoroperator= (const Subscriptor &)
 
Subscriptoroperator= (Subscriptor &&)
 
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)
 

Static Public Member Functions

static std::vector< Polynomials::Polynomial< double > > generate_complete_basis (const unsigned int degree)
 
- Static Public Member Functions inherited from Subscriptor
static::ExceptionBase & ExcInUse (int arg1, char *arg2, std::string &arg3)
 
static::ExceptionBase & ExcNoSubscriber (char *arg1, char *arg2)
 

Static Private Member Functions

static const std::vector< double > get_coefficients (const unsigned int k)
 

Additional Inherited Members

- Protected Member Functions inherited from Polynomials::Polynomial< double >
void transform_into_standard_form ()
 
- Static Protected Member Functions inherited from Polynomials::Polynomial< double >
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)
 
- Protected Attributes inherited from Polynomials::Polynomial< double >
std::vector< double > coefficients
 
bool in_lagrange_product_form
 
std::vector< double > lagrange_support_points
 
double lagrange_weight
 

Detailed Description

Class implementing the integrated Legendre polynomials described in the PhD thesis of Sabine Zaglmayr.

This class was written based upon the existing deal.II Legendre class as a base, but with the coefficents adjusted so that the recursive formula is for the integrated Legendre polynomials described in the PhD thesis of Sabine Zaglmayr. The polynomials can be generated recursively from:

However, it is also possible to generate them directly from the Legendre polynomials:

\(L_{n} = \frac{l_{n} - l_{n-2}}{2n-1)}\)

Definition at line 48 of file polynomials_integrated_legendre_sz.h.

Constructor & Destructor Documentation

IntegratedLegendreSZ::IntegratedLegendreSZ ( const unsigned int  p)

Constructor generating the coefficients of the polynomials at degree p.

Definition at line 21 of file polynomials_integrated_legendre_sz.cc.

Member Function Documentation

std::vector< Polynomials::Polynomial< double > > IntegratedLegendreSZ::generate_complete_basis ( const unsigned int  degree)
static

Returns the complete set of Integrated Legendre polynomials up to the given degree.

Definition at line 75 of file polynomials_integrated_legendre_sz.cc.

const std::vector< double > IntegratedLegendreSZ::get_coefficients ( const unsigned int  k)
staticprivate

Main function to compute the co-efficients of the polynomial at degree p.

Definition at line 28 of file polynomials_integrated_legendre_sz.cc.


The documentation for this class was generated from the following files: