COMPARISON BETWEEN GLOBAL, CLASSICAL DOMAIN DECOMPOSITION AND LOCAL, SINGLE AND DOUBLE COLLOCATION METHODS BASED ON RBF INTERPOLATION FOR SOLVING CONVECTION-DIFFUSION EQUATION

Gail Gutierrez () and Whady Florez ()
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Gail Gutierrez: GISICO, Universidad Popular del Cesar, Campus Hurtado, Edif. Adm. Ofic. 205, Valledupar, Cesar, Colombia
Whady Florez: IET, Universidad Pontificia Bolivariana, Cir 1–73-34, Medellin, Antioquia, Colombia

International Journal of Modern Physics C (IJMPC), 2008, vol. 19, issue 11, 1737-1751

Abstract: This work presents a performance comparison of several meshless RBF formulations for convection-diffusion equation with moderate-to-high Peclet number regimes. For the solution of convection-diffusion problems, several comparisons between global (full-domain) meshless RBF methods and mesh-based methods have been presented in the literature. However, in depth studies between new local RBF collocation methods and full-domain symmetric RBF collocation methods are not reported yet. The RBF formulations included: global symmetric method, symmetric double boundary collocation method, additive Schwarz domain decomposition method (DDM) when it is incorporated into two anterior approaches, and local single and double collocation methods. It can be found that the accuracy of solutions deteriorates asPeincreases, if no special treatment is used. From the numerical tests, it seems that the local methods, especially the derived double collocation technique incorporating PDE operator, are more effective than full domain approaches even with iterative DDM in solving moderate-to-high Pe convection-diffusion problems subject to mixed boundary conditions.

Keywords: Radial basis function; double collocation; domain decomposition methods; convection-diffusion equation; 11.25.Hf; 123.1K (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1142/S0129183108013102

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