Paper Info
Title
Conformal mapping for the efficient MFS solution of Dirichlet boundary value problems
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.
Year
DOI
Venue
2008
10.1007/s00607-008-0012-9
Computing
Keywords
DocType
Volume
. method of fundamental solutions,laplace equation,fast fourier,simply-connected domain,unit disk,annular domain,Dirichlet boundary value problem,circulant matrices.,doubly-connected domain,harmonic Dirichlet problem,efficient MFS solution,numerical example,fundamental solution,conformal mapping
Journal
83
Issue
ISSN
Citations 
1
1436-5057
2
PageRank 
References 
Authors
0.45
3
2
Name
Order
Citations
PageRank
Andreas Karageorghis120447.54
Yiorgos-Sokratis Smyrlis2418.44