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Compact Local IRBF and Domain Decomposition Method for solving PDEs using a Distributed termination detection based parallel algorithm

N. Pham-Sy1, C.-D. Tran1, T.-T. Hoang-Trieu1, N. Mai-Duy1, T. Tran-Cong1
Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, QLD 4350, Australia.

Computer Modeling in Engineering & Sciences 2013, 92(1), 1-31. https://doi.org/10.3970/cmes.2013.092.001

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.

Keywords

Integrated RBFs, Compact Local Stencils, Domain Decomposition Method, Parallel Algorithm, Distributed Termination Detection

Cite This Article

Pham-Sy, N., Tran, C., Hoang-Trieu, T., Mai-Duy, N., 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 & Sciences, 92(1), 1–31.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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