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.