Mesh-free radial basis function network methods with domain decomposition for approximation of functions and numerical solution of Poisson's equations

Mai-Duy, Nam and Tran-Cong, Thanh (2002) Mesh-free radial basis function network methods with domain decomposition for approximation of functions and numerical solution of Poisson's equations. Engineering Analysis with Boundary Elements, 26 (2). pp. 133-156. ISSN 0955-7997

Abstract

This paper presents the combination of new mesh-free radial basis function network (RBFN) methods and domain decomposition (DD) technique for approximating functions and solving Poisson's equations. The RBFN method allows numerical approximation of functions and solution of partial differential equations (PDEs) without the need for a traditional ‘finite element’-type (FE) mesh while the combined RBFN–DD approach facilitates coarse-grained parallelisation of large problems. Effect of RBFN parameters on the quality of approximation of function and its derivatives is investigated and compared with the case of single domain. In solving Poisson's equations, an iterative procedure is employed to update unknown boundary conditions at interfaces. At each iteration, the interface boundary conditions are first estimated by using boundary integral equations (BIEs) and subdomain problems are then solved by using the RBFN method. Volume integrals in standard integral equation representation (IE), which usually require volume discretisation, are completely eliminated in order to preserve the mesh-free nature of RBFN methods. The numerical examples show that RBFN methods in conjunction with DD technique achieve not only a reduction of memory requirement but also a high accuracy of the solution.


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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: mesh-free radial basis function network methods; domain decomposition; boundary integral equations; function approximation; Poisson's equation
Fields of Research : 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
01 Mathematical Sciences > 0101 Pure Mathematics > 010110 Partial Differential Equations
09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: 10.1016/S0955-7997(01)00092-3
URI: http://eprints.usq.edu.au/id/eprint/14352

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