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

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...

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Vydáno v:	Engineering analysis with boundary elements Ročník 26; číslo 2; s. 133 - 156
Hlavní autoři:	Mai-Duy, Nam, Tran-Cong, Thanh
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Oxford Elsevier Ltd 01.02.2002 Elsevier
Témata:	Boundary integral equations Computational techniques Computers in experimental physics Domain decomposition Exact sciences and technology Function approximation Instruments, apparatus, components and techniques common to several branches of physics and astronomy Mathematical methods in physics Mesh-free radial basis function network methods Neural networks, fuzzy logic, artificial intelligence Physics Poisson's equation Poisson's equation Function approximation Domain decomposition Mesh-free radial basis function network methods Boundary integral equations Meshed network Partial differential equations Boundary conditions Poisson equation Boundary integral method Numerical method Function decomposition Finite element method Integral equations Neural networks Meshless method Coarse grain structure Modelling Memory effect
ISSN:	0955-7997, 1873-197X
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Shrnutí:	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.
Bibliografie:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0955-7997 1873-197X
DOI:	10.1016/S0955-7997(01)00092-3