Conformal Mapping for the Efficient Solution of Poisson Problems with the Kansa-RBF Method

Authors

Xiao-Yan Liu, Taiyuan University of Technology
C.S. Chen, University of Southern MississippiFollow
Andreas Karageorghis, University of CyprusFollow

Document Type

Article

Publication Date

6-2017

Department

Mathematics

Abstract

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.

Publication Title

Journal of Scientific Computing

Volume

71

Issue

3

First Page

1035

Last Page

1061

Recommended Citation

Liu, X., Chen, C., Karageorghis, A. (2017). Conformal Mapping for the Efficient Solution of Poisson Problems with the Kansa-RBF Method. Journal of Scientific Computing, 71(3), 1035-1061.
Available at: https://aquila.usm.edu/fac_pubs/17679