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Numerical Determination of the Resonance Frequencies and Eigenmodes Using the MFS

Alves, Carlos J. S.; Antunes, Pedro R. S.

Computational Methods, Ed. Liu, GR et al., ISBN 978-1-4020-3953-9 (2006), 1385-1389

In this work we present a numerical algorithm for the determination of the eigenvalues and eigenfunctions associated to the Dirichlet problem for the Laplacian, in a bounded or in an exterior domain. The determination of higher eigenfrequencies is a well-known numerical problem, that has been addressed with other numerical methods. Here we propose to use the method of fundamental solutions. Since the MFS produces highly ill conditioned matrices, a particular technique was derived to overcome the difficulty of determining accurately those eigenfrequencies. Extensive numerical simulations will be presented.