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Domain Decomposition for Time-Dependent Problems Using Radial Based Meshless Methods

Domain Decomposition for Time-Dependent Problems Using Radial Based Meshless Methods
Domain Decomposition for Time-Dependent Problems Using Radial Based Meshless Methods
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.
0749-159X
38-59
Chinchapatnam, P.P.
61221cab-afae-46d5-a6ea-14eb472d5522
Djidjeli, K.
94ac4002-4170-495b-a443-74fde3b92998
Nair, P.B.
d4d61705-bc97-478e-9e11-bcef6683afe7
Chinchapatnam, P.P.
61221cab-afae-46d5-a6ea-14eb472d5522
Djidjeli, K.
94ac4002-4170-495b-a443-74fde3b92998
Nair, P.B.
d4d61705-bc97-478e-9e11-bcef6683afe7

Chinchapatnam, P.P., Djidjeli, K. and Nair, P.B. (2007) Domain Decomposition for Time-Dependent Problems Using Radial Based Meshless Methods. Numerical Methods for Partial Differential Equations, 23 (1), 38-59. (doi:10.1002/num.20171).

Record type: Article

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.

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Submitted date: July 2004
Published date: 2007

Identifiers

Local EPrints ID: 38132
URI: http://eprints.soton.ac.uk/id/eprint/38132
ISSN: 0749-159X
PURE UUID: 796f6a62-d6b5-4373-a6e0-a38faab58c41

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Date deposited: 05 Jun 2006
Last modified: 15 Jul 2019 19:03

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Contributors

Author: P.P. Chinchapatnam
Author: K. Djidjeli
Author: P.B. Nair

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