Compact local IRBF and domain decomposition method for solving PDEs using a distributed termination detection based parallel algorithm

Pham-Sy, N. and Tran, C.-D. and Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran-Cong, T. (2013) Compact local IRBF and domain decomposition method for solving PDEs using a distributed termination detection based parallel algorithm. CMES: Computer Modeling in Engineering and Sciences, 92 (1). pp. 1-31. ISSN 1526-1492

Abstract

Compact Local Integrated Radial Basis Function (CLIRBF) methods based on Cartesian grids can be effective numerical methods for solving partial differential equations (PDEs) for fluid flow problems. The combination of the domain decomposition method and function approximation using CLIRBF methods yields an effective coarse-grained parallel processing approach. This approach has enabled not only each sub-domain in the original analysis domain to be discretised by a separate CLIRBF network but also compact local stencils to be independently treated. The present algorithm, namely parallel CLIRBF, achieves higher throughput in solving large scale problems by, firstly, parallel processing of sub-regions which constitute the original domain and, secondly, accelerating the convergence rate within each sub-region using groups of CLIRBF stencils in which function approximations are carried out by parallel processes. The procedure is illustrated with several numerical examples of PDEs and lid-driven cavity problem using Message Passing Interface supported by MATLAB.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Copyright © 2013 Tech Science Press. Published version deposited in accordance with the copyright policy of the publisher.
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - No Department
Date Deposited: 05 Aug 2013 02:36
Last Modified: 12 Nov 2015 05:45
Uncontrolled Keywords: compact local stencils; distributed termination detection; domain decomposition method; integrated RBFs; parallel algorithm
Fields of Research : 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
01 Mathematical Sciences > 0102 Applied Mathematics > 010201 Approximation Theory and Asymptotic Methods
08 Information and Computing Sciences > 0805 Distributed Computing > 080501 Distributed and Grid Systems
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: 10.3970/cmes.2013.092.001
URI: http://eprints.usq.edu.au/id/eprint/23851

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