Preconditioned rotated iterative methods in the solution of elliptic partial differential equation

Abstract

A second-order finite difference scheme derived from rotated discretisation formula is employed in conjunction with a preconditioner to obtain highly accurate and fast numerical solution of the two-dimensional elliptic partial differential equation. The use of a ‘splitting’ preconditioning strategy will be shown to improve the spectral properties of the matrix of the linear system resulting from this discretisation by minimising the eigenvalue spectrum of the transformed matrix. The application of this technique to several acceleration iterative methods, such as Simultaneous displacement, Richardson's and Chebyshev accelerated methods, are presented and discussed.

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Keywords:

• Preconditioning techniques
• Finite difference
• Iterative methods
• Elliptic equations

Acknowledgement

This work was carried out under the fellowship programme of the Association of Commonwealth Universities for N. M. Ali.

Notes

E-mail: [email protected]