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Some observations on unsymmetric radial basis function collocation methods for convection–diffusion problems
Author(s) -
Li Jichun,
Chen C. S.
Publication year - 2003
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.722
Subject(s) - collocation (remote sensing) , radial basis function , collocation method , diffusion , domain (mathematical analysis) , function (biology) , domain decomposition methods , mathematics , convection–diffusion equation , computer science , mathematical analysis , physics , thermodynamics , differential equation , artificial intelligence , finite element method , ordinary differential equation , machine learning , evolutionary biology , biology , artificial neural network
In this paper, we re‐investigate the unsymmetric radial basis function (RBF) collocation method for solving convection–diffusion problems with high Péclet number as in Power and Barraco ( Computers and Mathematics with Applications 2002; 43: 551). By testing different RBFs and different numbers of nodes, we found that the unsymmetric method can still solve high Péclet number problems reasonably well by using more nodes and domain decomposition techniques. Compared to solving one large problem, the domain decomposition method is shown to be very efficient and can improve the accuracy especially when the Péclet number is not that high. From our tests, it seems that the RBFs r 4 ln r and r 8 ln r are not very stable, while r 6 ln r , r 5 and r 7 perform very well. Copyright © 2003 John Wiley & Sons, Ltd.