Preconditioned variational methods on rotated finite difference discretisation

Abstract

Due to their rapid convergence properties, recent focus on iterative methods in the solution of linear system has seen a flourish on the use of gradient techniques which are primarily based on global minimisation of the residual vectors. In this paper, we conduct an experimental study to investigate the performance of several preconditioned gradient or variational techniques to solve a system arising from the so-called rotated (skewed) finite difference discretisation in the solution of elliptic partial differential equations (PDEs). The preconditioned iterative methods consist of variational accelerators, namely the steepest descent and conjugate gradient methods, applied to a special matrix ‘splitting’ preconditioned system. Several numerical results are presented and discussed.

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Keywords:

• Preconditioning techniques
• Finite difference
• Gradient 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]