On Cyclic Reduction and Finite Difference Schemes

Jun Zhang
Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506-0046, USA

Jules Kouatchou
School of Engineering
Morgan State University
Baltimore, MD 21251, USA

Mohamed Othman
Department of Computer Science
University Putra Malaysia
43400 UPM Serdang, Selangor D.E., Malaysia

Abstract

We investigate a family of finite difference schemes for discretizing the two dimensional Poisson equation on both the standard and the reduced grids. We study the relation between the cyclic reduction method and the discretization schemes on different grids. The spectral radii of the Jacobi iteration matrices, and the truncation errors of, different discretization schemes are compared analytically and numerically.


Key words: discretization, finite difference, cyclic reduction.


This paper has been published in Journal of Computational and Applied Mathematics, Vol. 145, No. 1, pp. 213-222 (2002). Technical Report 292-99, Department of Computer Science, University of Kentucky, Lexington, KY, 1999. This research was supported in part by the U.S. National Science Foundation under the grant CCR-9902022, in part by the University of Kentucky Center for Computational Sciences, and in part by NASA under the grant No. NAGS-3508.