Development of parallel algorithm for boundary value problems using compact local integrated RBFN and domain decomposition

Pham-Sy, N. and Hoang-Trieu, T.-T. and Tran, C.-D. ORCID: https://orcid.org/0000-0002-1011-4226 and Mai-Duy, N. and Tran-Cong, T. (2012) Development of parallel algorithm for boundary value problems using compact local integrated RBFN and domain decomposition. In: 4th International Conference on Computational Methods (ICCM 2012), 25-28 Nov 2012, Gold Coast, Australia.

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Abstract

Compact Local Integrated Radial Basis Function (CLIRBF) methods based on Cartesian grids can be effective numerical methods for solving Elliptic Partial Differential Equations (EPDEs) for fluid flow problems. The combination of the domain decomposition technique and function approximation using CLIRBF methods yields an effective coarse-grained parallel processing approach. This feature 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 comprise 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 EPDEs using Message Passing Interface (MPI) supported by MATLAB.

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Item Type:	Conference or Workshop Item (Commonwealth Reporting Category E) (Paper)
Refereed:	Yes
Item Status:	Live Archive
Additional Information:	No evidence of copyright restrictions preventing deposit.
Faculty/School / Institute/Centre:	Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering (Up to 30 Jun 2013)
Faculty/School / Institute/Centre:	Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering (Up to 30 Jun 2013)
Date Deposited:	15 Apr 2013 00:19
Last Modified:	18 Sep 2014 03:40
Uncontrolled Keywords:	integrated RBFs; compact local stencils; domain decomposition; parallel algorithm
Fields of Research (2008):	01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations 09 Engineering > 0915 Interdisciplinary Engineering > 091508 Turbulent Flows 01 Mathematical Sciences > 0101 Pure Mathematics > 010110 Partial Differential Equations
Socio-Economic Objectives (2008):	E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
URI:	http://eprints.usq.edu.au/id/eprint/23076

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