On Cyclic Reduction and Finite Difference Schemes

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. Mathematics Subject Classification: 65N06, 65N22, 65F10. Technical Report No. 292-99, Department of Computer Science, University of Kentucky, Lexington, KY, 1999. y E-mail: jzhang@cs.uky.edu. URL: jzhang@cs.uky.edu/~jzhang. The research of this author was supported in part by the U.S. National Science Foundation under the grant CCR-9902022, and in part by the University of Kentucky Center for Computational Sciences. z E-mail: kouatch@pecos1.gsfc.nasa.gov. URL: http://cesdis1.gsfc.nasa.gov/~kouatch. The re..