Efficient implementation of the MFS: The three scenarios

Authors:
Yiorgos-Sokratis Smyrlis;Andreas Karageorghis
Affiliations:
Department of Mathematics and Statistics, University of Cyprus, P.O.Box 20537, 1678 Nicosia/ωa, Cyprus;Department of Mathematics and Statistics, University of Cyprus, P.O.Box 20537, 1678 Nicosia/ωa, Cyprus
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 1
Cited 3

Some Aspects of the Method of Fundamental Solutions for Certain Harmonic Problems

Journal of Scientific Computing

The under-determined version of the MFS: Taking more sources than collocation points

Applied Numerical Mathematics
A meshfree numerical method for acoustic wave propagation problems in planar domains with corners and cracks

Journal of Computational and Applied Mathematics
Comparing seven spectral methods for interpolation and for solving the Poisson equation in a disk: Zernike polynomials, Logan-Shepp ridge polynomials, Chebyshev-Fourier Series, cylindrical Robert functions, Bessel-Fourier expansions, square-to-disk conformal mapping and radial basis functions

Journal of Computational Physics

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Abstract

In this study we investigate the approximation of the solutions of harmonic problems subject to Dirichlet boundary conditions by the Method of Fundamental Solutions (MFS). In particular, we study the application of the MFS to Dirichlet problems in a disk. The MFS discretization yields systems which possess special features which can be exploited by using Fast Fourier transform (FFT)-based techniques. We describe three possible formulations related to the ratio of boundary points to sources, namely, when the number of boundary points is equal, larger and smaller than the number of sources. We also present some numerical experiments and provide an efficient MATLAB implementation of the resulting algorithms.