The method of fundamental solutions with dual reciprocity for diffusion and diffusion-convection using subdomains

The method of fundamental solutions (MFS), first proposed in the 1960s, has recently reappeared in the literature and solutions of an extraordinary ac curacy have been reported using relatively few data points. The method requ ires no mesh and therefore no integration, and has been recently combined w ith dual reciprocity method (DRM) for treating inhomogeneous terms. The obj ective of this paper is the combination of the two methods for treating con vective terms which are derivatives of the problem variable. First the form ulation of the methods for mixed Neumann-Dirichlet boundary conditions is c onsidered, as both these types of boundary condition are necessary for this type of problem. Next a formulation for the usual Crank-Nickleson and Gale rkin time-stepping procedures is obtained for both diffusion and diffusion- convection and the use of the subdomain technique with MFS is considered. F inally results obtained for some test problems are presented including a di ffusion convection problem with variable velocity using both a single domai n and a division into subregions, the convective terms being modeled using DRM. Results are compared with exact solutions and in some cases with DRBEM examples from the literature. (C) 2000 Elsevier Science Ltd. All rights re served.