Conformal mapping for the efficient MFS solution of Dirichlet boundary value problems
Date
2008ISSN
0010485XSource
Computing (Vienna/New York)Volume
83Issue
1Pages
124Google Scholar check
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In this work, we use conformal mapping to transform harmonic Dirichlet problems of Laplace's equation which are defined in simplyconnected 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 doublyconnected 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. © 2008 SpringerVerlag.
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