The Method of Fundamental Solutions Applied to the Calculation of Eigenfrequencies and Eigenmodes of 2D Simply Connected Shapes
Carlos J. S. Alves and Pedro R. S. Antunes

doi:10.3970/cmc.2005.002.251
Source CMC: Computers, Materials, & Continua, Vol. 2, No. 4, pp. 251-266, 2005
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Keywords Eigenfrequencies, Eigenmodes, Acoustic waves, Method of fundamental solutions
Abstract In this work we show the application of the Method of Fundamental Solutions (MFS) in the determination of eigenfrequencies and eigenmodes associated to wave scattering pro\discretionary {-}{}{}blems. This meshless method was already applied to simple geometry domains with Dirichlet boundary conditions (cf. \relax \begingroup \catcode `\ 12\relax \catcode `\\12\relax \catcode `\$12\relax \catcode `\&12\relax \catcode `\#12\relax \catcode `\^12\relax \catcode `\_12\relax \catcode `\%12\relax \catcode `\~12\relax \endgroup \relax \cite *{Karag}) and to multiply connected domains (cf. \relax \begingroup \catcode `\ 12\relax \catcode `\\12\relax \catcode `\$12\relax \catcode `\&12\relax \catcode `\#12\relax \catcode `\^12\relax \catcode `\_12\relax \catcode `\%12\relax \catcode `\~12\relax \endgroup \relax \cite *{JTChenMFS}). Here we show that a particular choice of point-sources can lead to very good results for a fairly gene\discretionary {-}{}{}ral type of domains. Simulations with Neumann boundary condition are also considered.
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