A fast convergent iterative boundary element method on PVM cluster

Mai-Duy, N. and Nguyen-Hong, P. and Tran-Cong, T. (1998) A fast convergent iterative boundary element method on PVM cluster. Engineering Analysis with Boundary Elements , 22 (4). pp. 307-316. ISSN 0955-7997


This paper reports a fast convergent boundary element method on a Parallel Virtual Machine (PVM) (Geist et al., PVM: Parallel Virtual Machine, A Users' Guide and Tutorial for Networked Parallel Computing. MIT Press, Cambridge, 1994) cluster using the SIMD computing model (Single Instructions Multiple Data). The method uses the strategy of subdividing the domain into a number of smaller subdomains in order to reduce the size of the system matrix and to achieve overall speedup. Unlike traditional subregioning methods, where equations from all subregions are assembled into a single linear algebraic system, the present scheme is iterative and each subdomain is handled by a separate PVM node in parallel. The iterative nature of the overall solution procedure arises due to the introduction of the artificial boundaries. However, the system equations for each subdomain is now smaller and solved by direct Gaussian elimination within each iteration. Furthermore, the boundary conditions at the artificial interfaces are estimated from the result of the previous iteration by a reapplication of the boundary integral equation for internal points. This method provides a consistent mechanism for the specification of boundary conditions on artificial interfaces, both initially and during the iterative process. The method is fast convergent in comparison with other methods in the literature. The achievements of this method are therefore: (a) simplicity and consistency of methodology and implementation; (b) more flexible choice of type of boundary conditions at the artificial interfaces; (c) fast convergence; and (d) the potential to solve large problems on very affordable PVM clusters. The present parallel method is suitable where (a) one has a distributed computing environment; (b) the problem is big enough to benefit from the speedup achieved by coarse-grained parallelisation; and (c) the subregioning is such that communication overhead is only a small percentage of total computation time.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 30 Nov 2007 11:47
Last Modified: 05 Mar 2018 06:55
Uncontrolled Keywords: boundary element method on PVM cluster; iterative boundary element method; parallel boundary element method
Fields of Research : 10 Technology > 1005 Communications Technologies > 100503 Computer Communications Networks
01 Mathematical Sciences > 0101 Pure Mathematics > 010108 Operator Algebras and Functional Analysis
08 Information and Computing Sciences > 0801 Artificial Intelligence and Image Processing > 080111 Virtual Reality and Related Simulation
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970110 Expanding Knowledge in Technology
Identification Number or DOI: 10.1016/S0955-7997(98)00071-X
URI: http://eprints.usq.edu.au/id/eprint/13744

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