(1) Department of Mathematics and Statistics, University of Cyprus, 1678 Nicosia, Cyprus
Abstract:
In this work, we use conformal mapping to transform harmonic Dirichlet problems of Laplace’s equation which are defined in
simply-connected domains into harmonic Dirichlet problems that are defined in the unit disk. We then solve the resulting harmonic
Dirichlet problems efficiently using the method of fundamental solutions (MFS) in conjunction with fast fourier transforms
(FFTs). This technique is extended to harmonic Dirichlet problems in doubly-connected domains which are now mapped onto annular
domains. The solution of the resulting harmonic Dirichlet problems can be carried out equally efficiently using the MFS with
FFTs. Several numerical examples are presented.