LagrangeJacobi1D Class Reference

Calculate the 1D Lagrange polynomials and the first derivative using Jacobi polynomials. More...

#include <LagrangeJacobi1D.h>

List of all members.

Public Member Functions
void	GetPolynomialValue (unsigned long PolyOrder, QuadCollocType_E QuadratureType, unsigned long Alpha, unsigned long Beta, double *const CollocCoordinates, double *const Coordinates, unsigned long NumCoordinates, double *Phi)
	Calculates Lagrange polynomials on the values given in Coordinates for the collocation points CollocCoordinates in terms of zeros of Jacobi polynomials of mixed weights Alpha and Beta. Procedure is based on the initial implementation by Thais Godoy Vazquez.
void	Get1stDerivative (unsigned long PolyOrder, QuadCollocType_E QuadratureType, unsigned long Alpha, unsigned long Beta, double *const CollocCoordinates, double *const Coordinates, unsigned long NumCoordinates, double *dPhi)
	Calculates the first derivatives of Lagrange polynomials on the values given in Coordinates for the collocation points CollocCoordinates in terms of zeros of Jacobi polynomials of mixed weights Alpha and Beta. Procedure is based on the initial implementation by Thais Godoy Vazquez.
void	Get2ndDerivative (unsigned long PolyOrder, QuadCollocType_E QuadratureType, unsigned long Alpha, unsigned long Beta, double *const CollocCoordinates, double *const Coordinates, unsigned long NumCoordinates, double *d2Phi)
	Calculates the second derivatives of Lagrange polynomials on the values given in Coordinates for the collocation points CollocCoordinates in terms of zeros of Jacobi polynomials of mixed weights Alpha and Beta. Procedure is based on the initial implementation by Thais Godoy Vazquez.

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Detailed Description

Calculate the 1D Lagrange polynomials and the first derivative using Jacobi polynomials.

Author:

Junior Cintra Maurcio

Date:

May/12/2009

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Member Function Documentation

void LagrangeJacobi1D::Get1stDerivative	(	unsigned long	PolyOrder,
		QuadCollocType_E	QuadratureType,
		unsigned long	Alpha,
		unsigned long	Beta,
		double *const	CollocCoordinates,
		double *const	Coordinates,
		unsigned long	NumCoordinates,
		double *	dPhi
	)

Calculates the first derivatives of Lagrange polynomials on the values given in Coordinates for the collocation points CollocCoordinates in terms of zeros of Jacobi polynomials of mixed weights Alpha and Beta. Procedure is based on the initial implementation by Thais Godoy Vazquez.

Parameters:

[in]	PolyOrder	: Polynomial order;
[in]	CollocationType	: Type of collocation rule 'GAUSS_JACOBI', 'GAUSS_LEGENDRE', 'GAUSS_RADAU_JACOBI', 'GAUSS_RADAU_LEGENDRE', 'GAUSS_LOBATTO_JACOBI', 'GAUSS_LOBATTO_LEGENDRE', 'EQUALLY_SPACED'.
[in]	Alpha,Beta	: Weights of Jacobi polynomials (integers and greater than -1) for the collocation points
[in]	Coordinates	: Coordinates on which the polynomial values are calculated
[in]	CollocCoordinates	: Collocation points coordinates (Element nodes coordinates).
[in]	NumCoordinates	- number of coordinates where the polynomials are calculated.
[out]	dPhi,:	Matrix with the first derivative polynomial values. The rows indicate the polynomials and the columns store the values.

void LagrangeJacobi1D::Get2ndDerivative	(	unsigned long	PolyOrder,
		QuadCollocType_E	QuadratureType,
		unsigned long	Alpha,
		unsigned long	Beta,
		double *const	CollocCoordinates,
		double *const	Coordinates,
		unsigned long	NumCoordinates,
		double *	d2Phi
	)

Calculates the second derivatives of Lagrange polynomials on the values given in Coordinates for the collocation points CollocCoordinates in terms of zeros of Jacobi polynomials of mixed weights Alpha and Beta. Procedure is based on the initial implementation by Thais Godoy Vazquez.

Parameters:

[in]	PolyOrder	: Polynomial order;
[in]	CollocationType	: Type of collocation rule 'GAUSS_JACOBI', 'GAUSS_LEGENDRE', 'GAUSS_RADAU_JACOBI', 'GAUSS_RADAU_LEGENDRE', 'GAUSS_LOBATTO_JACOBI', 'GAUSS_LOBATTO_LEGENDRE', 'EQUALLY_SPACED'.
[in]	Alpha,Beta	: Weights of Jacobi polynomials (integers and greater than -1) for the collocation points
[in]	Coordinates	: Coordinates on which the polynomial values are calculated
[in]	CollocCoordinates	: Collocation points coordinates (Element nodes coordinates).
[in]	NumCoordinates	- number of coordinates where the polynomials are calculated.
[out]	d2Phi,:	Matrix with the second derivative polynomial values. The rows indicate the polynomials and the columns store the values.

void LagrangeJacobi1D::GetPolynomialValue	(	unsigned long	PolyOrder,
		QuadCollocType_E	QuadratureType,
		unsigned long	Alpha,
		unsigned long	Beta,
		double *const	CollocCoordinates,
		double *const	Coordinates,
		unsigned long	NumCoordinates,
		double *	Phi
	)

Calculates Lagrange polynomials on the values given in Coordinates for the collocation points CollocCoordinates in terms of zeros of Jacobi polynomials of mixed weights Alpha and Beta. Procedure is based on the initial implementation by Thais Godoy Vazquez.

Parameters:

[in]	PolyOrder	: Polynomial order;
[in]	CollocationType	: Type of collocation rule 'GAUSS_JACOBI', 'GAUSS_LEGENDRE', 'GAUSS_RADAU_JACOBI', 'GAUSS_RADAU_LEGENDRE', 'GAUSS_LOBATTO_JACOBI', 'GAUSS_LOBATTO_LEGENDRE', 'EQUALLY_SPACED'.
[in]	Alpha,Beta	: Weights of Jacobi polynomials (integers and greater than -1) for the collocation points
[in]	Coordinates	: Coordinates on which the polynomial values are calculated
[in]	CollocCoordinates	: Collocation points coordinates (Element nodes coordinates).
[in]	NumCoordinates	- number of coordinates where the polynomials are calculated for the Collocation points.
[out]	Phi,:	Matrix with the polynomial values. The rows indicate the polynomials and the columns store the values.

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

• include/interpolation/polynomials1d/LagrangeJacobi1D.h
• src/interpolation/polynomials1d/LagrangeJacobi1D.cpp