Domain decomposition for time-dependent problems using radial based meshless methods

✍ Scribed by Phani P. Chinchapatnam; K. Djidjeli; Prasanth B. Nair

• Publisher: John Wiley and Sons
• Year: 2006
• Tongue: English
• Weight: 986 KB
• Volume: 23
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/num.20171

✦ Synopsis

Abstract

In this article, we present meshless overlapping Schwarz additive and multiplicative domain decomposition schemes for time‐dependent problems using radial basis functions. The proposed schemes are compared with the global radial basis function collocation method and an explicit multizone domain decomposition method (Wong et al., Comput Math Appl 37 (1999), 23–43) by solving an unsteady convection‐diffusion problem for various Peclet numbers. Stability analysis of the presented schemes suggest that for radial basis functions incorporating a free shape parameter, the freedom of varying the shape parameter decreases with increase in the number of collocation points. Numerical studies show that the ill‐conditioning problem of global radial basis function collocation method is reduced by the proposed Schwarz schemes. Also, with an increase in the number of subdomains the efficiency of the Schwarz schemes increases with a slight loss in the accuracy. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007