Accession Number : ADA304195

Title :   Local Multiplicative Schwarz Algorithms for Convection-Diffusion Equations.

Corporate Author : INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA

Personal Author(s) : Cai, Xiao-Chuan ; Sarkis, Marcus

PDF Url : ADA304195

Report Date : DEC 1995

Pagination or Media Count : 16

Abstract : We develop a new class of overlapping Schwarz type algorithms for solving scalar convection-diffusion equations discretized by finite element or finite difference methods. The preconditioners consist of two components, namely, the usual two-level additive Schwarz preconditioner and the sum of some quadratic terms constructed by using products of ordered neighboring subdomain preconditioners. The ordering of the subdomain preconditioners is determined by considering the direction of the flow. We prove that the algorithms are optimal in the sense that the convergence rates are independent of the mesh size, as well as the number of subdomains. We show by numericaL examples that the new algorithms are less sensitive to the direction of the flow than either the classical multiplicative Schwarz algorithms, and converge faster than the additive Schwarz algorithms. Thus, the new algorithms are more suitable for fluid flow applications than the classical additive or multiplicative Schwarz algorithms. (AN)

Descriptors :   *ALGORITHMS, *FINITE ELEMENT ANALYSIS, MATHEMATICAL MODELS, LINEAR SYSTEMS, OPTIMIZATION, EQUATIONS OF MOTION, FINITE DIFFERENCE THEORY, BOUNDARY VALUE PROBLEMS, PARTIAL DIFFERENTIAL EQUATIONS, QUADRATIC EQUATIONS, CONVERGENCE, NUMERICAL METHODS AND PROCEDURES, ITERATIONS, LAPLACE TRANSFORMATION.

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE