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Meshfree explicit local radial basis function collocation method for diffusion problems. (English) Zbl 1168.41003
This paper formulates a simple explicit local version of the classical meshless radial basis function (RBF) collocation (Kansa) method [cf. E. J. Kansa, Comput. Math. Appl. 19, No. 8–9, 147–161 (1990; Zbl 0850.76048)]. The discussion is limited to solving the heat diffusion equation. The collocation is made locally over a set of overlapping domains of influence and the time-stepping is performed in an explicit way. Only small systems of linear equations with the dimension of the number of nodes included in the domain of influence have to be solved for each node. The boundary value problem (NAFEMS test) associated with the steady temperature field with simultaneous involvement of the Dirichlet, Neumann and Robin boundary conditions on a rectangle and the initial value problem associated with the Dirichlet jump problem on a square are discussed as numerical examples.

MSC:
41A63 Multidimensional problems
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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