Paper Info
Title
The method of fundamental solutions for elliptic problems in circular domains with mixed boundary conditions
Abstract
We apply the method of fundamental solutions (MFS) for the solution of harmonic and biharmonic problems in circular domains subject to mixed boundary conditions. In contrast to the cases when boundary conditions of the same kind are prescribed on the whole boundary, for example, only Dirichlet conditions in the harmonic case, and Dirichlet and Neumann conditions in the biharmonic case, the resulting systems are neither circulant (harmonic case) nor block circulant (biharmonic case). However, by appropriately manipulating the matrices involved in the MFS discretization, the partial circulant/block circulant structure of these matrices can be exploited when certain iterative methods of solution are used for the solution of the resulting systems. This leads to efficient fast Fourier transform (FFT) algorithms which are tested on several numerical examples.
Year
DOI
Venue
2015
10.1007/s11075-014-9900-6
Numerical Algorithms
Keywords
Field
DocType
Laplace equation,Biharmonic equation,Method of fundamental solutions,Fast Fourier transforms,Primary 65N35,Secondary 65N80,65N38
Discretization,Boundary value problem,Mathematical optimization,Mathematical analysis,Iterative method,Dirichlet conditions,Laplace's equation,Circulant matrix,Method of fundamental solutions,Biharmonic equation,Mathematics
Journal
Volume
Issue
ISSN
68
1
1017-1398
Citations 
PageRank 
References 
1
0.37
7
Authors
1
Name
Order
Citations
PageRank
Andreas Karageorghis120447.54