Feel::dyna::Jacobi< T > Class Template Reference

1D Jacobi polynomial More...

#include <jacobi.hpp>

List of all members.

Public Types
Typedefs
typedef T	value_type
typedef Jacobi< T >	self_type
Public Member Functions
Constructors, destructor
	Jacobi (uint16_type N, value_type a=value_type(0.0), value_type b=value_type(0.0))
	Jacobi (Jacobi const &p)
	~Jacobi ()
Operator overloads
self_type &	operator= (self_type const &p)
value_type	operator() (value_type const &x) const
Accessors
uint16_type	degree () const
Mutators
void	setDegree (uint16_type N)
Methods
value_type	value (value_type const &x) const
value_type	derivate (value_type const &x) const

---

Detailed Description

template<typename T = double>
class Feel::dyna::Jacobi< T >

1D Jacobi polynomial

(excerpt from Karniadakis/Sherwin Appendix A) Jacobi polynomials are a family of polynomial to the singular Sturm-Liouville problem. A significant feature of these polynomials is that they are orthogonal in the interval with respect to the function

Several functions related to the one-dimensional jacobi polynomials: Evaluation, evaluation of derivatives, plus computation of the roots via Newton's method.

Author:

Christophe Prud'homme

See also:

Karniadakis and Sherwin "Spectral/hp element methods for CFD"

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Constructor & Destructor Documentation

template<typename T = double>

Feel::dyna::Jacobi< T >::Jacobi	(	uint16_type	N,
		value_type	a = value_type( 0.0 ),
		value_type	b = value_type( 0.0 )
	)		[inline]

default values for a and b give the special case of Legendre polynomials

---

Member Function Documentation

template<typename T >

Jacobi< T >::value_type Feel::dyna::Jacobi< T >::operator()

(

value_type const &

x

)

const

Evaluates the nth jacobi polynomial with weight parameters a,b at a point x. Recurrence relations implemented from the pseudocode given in Karniadakis and Sherwin, Appendix B

a and b are defaulted to 0 and the Jacobi polynomial is then the Legendre polynomial

Parameters:

x	point for polynomial evaluation

Returns:

the value of the jacobi polynomial at x

Referenced by Feel::dyna::Jacobi< T >::value().

template<typename T = double>

value_type Feel::dyna::Jacobi< T >::value

(

value_type const &

x

)

const [inline]

Evaluates the nth jacobi polynomial with weight parameters a,b at a point x. Recurrence relations implemented from the pseudocode given in Karniadakis and Sherwin, Appendix B

a and b are defaulted to 0 and the Jacobi polynomial is then the Legendre polynomial

Parameters:

x	point for polynomial evaluation

Returns:

the value of the jacobi polynomial at x

References Feel::dyna::Jacobi< T >::operator()().