Conformal Mapping for the Efficient Solution of Poisson Problems with the Kansa-RBF Method
AuthorLiu, X. -Y
Chen, C. S.
SourceJournal of Scientific Computing
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We consider the solution of Poisson Dirichlet problems in simply-connected irregular domains. These domains are conformally mapped onto the unit disk and the resulting Poisson Dirichlet problems are solved efficiently using a Kansa-radial basis function (RBF) method with a matrix decomposition algorithm (MDA). In a similar way, we treat Poisson Dirichlet and Poisson Dirichlet–Neumann problems in doubly-connected domains. These domains are mapped onto annular domains by a conformal mapping and the resulting Poisson Dirichlet and Poisson Dirichlet–Neumann problems are solved efficiently using a Kansa-RBF MDA. Several examples demonstrating the applicability of the proposed technique are presented. © 2016, Springer Science+Business Media New York.