Lobatto1D Class Reference

Class for 1D Lobatto polynomialsCalculates the Lobatto polynomials and their first and second derivatives. More...

#include <Lobatto1D.h>

List of all members.

Public Member Functions
void	GetPolynomialValue (unsigned long PolyOrder, double *Coordinates, unsigned long NumCoordinates, double *Phi)
	Calculates the 1D Lobatto polynomials of orders 0 to PolyOrder on the coordinates of the vector Coordinates = [x0 x1 x2 ...]'. The Lobatto polynomials are calculated using Jacobi polynomials as shown by C. Pozrikidis in "Introduction to finite and spectral element methods using MATLAB", pg 139.
void	Get1stDerivative (unsigned long PolyOrder, double *const Coordinates, unsigned long NumCoordinates, double *dPhi)
	Computes the first derivative of the Lobatto polynomials of orders 0 to PolyOrder on Coordinates.
void	Get2ndDerivative (unsigned long PolyOrder, double *const Coordinates, unsigned long NumCoordinates, double *d2Phi)
	Computes the second derivative of the Lobatto polynomials of orders 0 to PolyOrder on Coordinates.

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Detailed Description

Class for 1D Lobatto polynomialsCalculates the Lobatto polynomials and their first and second derivatives.

Author:

Bruno Barbosa O F Salles

Date:

Jun/5/2009

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Member Function Documentation

void Lobatto1D::Get1stDerivative	(	unsigned long	PolyOrder,
		double *const	Coordinates,
		unsigned long	NumCoordinates,
		double *	dPhi
	)

Computes the first derivative of the Lobatto polynomials of orders 0 to PolyOrder on Coordinates.

Parameters:

[in]	PolyOrder	: polynomial order
[in]	Coordinates	: coordinates on which the polynomial first derivative values are calculated.
[in]	NumCoordinates	- number of coordinates qhere the polynomials are calculated.
[out]	dPhi,:	Matrix with the first derivatives of Lobatto polynomials of orders 0 to PolyOrder calculated on Coordinates. The rows indicate the polynomial degrees and the columns store the values.

void Lobatto1D::Get2ndDerivative	(	unsigned long	PolyOrder,
		double *const	Coordinates,
		unsigned long	NumCoordinates,
		double *	d2Phi
	)

Computes the second derivative of the Lobatto polynomials of orders 0 to PolyOrder on Coordinates.

Parameters:

[in]	PolyOrder	: polynomial order
[in]	Coordinates	: coordinates on which the polynomial first derivative values are calculated.
[in]	NumCoordinates	- number of coordinates qhere the polynomials are calculated.
[out]	d2Phi,:	Matrix with the second derivatives of Lobatto polynomials of orders 0 to PolyOrder calculated on Coordinates. The rows indicate the polynomial degrees and the columns store the values.

void Lobatto1D::GetPolynomialValue	(	unsigned long	PolyOrder,
		double *	Coordinates,
		unsigned long	NumCoordinates,
		double *	Phi
	)

Calculates the 1D Lobatto polynomials of orders 0 to PolyOrder on the coordinates of the vector Coordinates = [x0 x1 x2 ...]'. The Lobatto polynomials are calculated using Jacobi polynomials as shown by C. Pozrikidis in "Introduction to finite and spectral element methods using MATLAB", pg 139.

Parameters:

[in]	PolyOrder	: polynomial order
[in]	Coordinates	: coordinates on which the polynomial values are calculated.
[in]	NumCoordinates	- number of coordinates where the polynomials are calculated.
[in]	Phi,:	Matix with Lobatto polynomials for orders 0 to PolyOrder calculated on Coordinates. The rows indicate the polynomial degrees and the columns store the values.

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

• include/interpolation/polynomials1d/Lobatto1D.h
• src/interpolation/polynomials1d/Lobatto1D.cpp