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2 Vibrations in Physical Systems

2 2004

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Weighted least-squares algorithms of the method of fundamental solutions

Smyrlis Y. S., Karageorghis A.

Vibrations in Physical Systems

2004

Vol. 21

339--348

We Study the Method of Fundamental Solutions (MPS) for the solution of certain elliptic boundary value problems. We propose least squares algorithms, when the number of collocation points is larger the number of singularities as well as in "the case in which the number of singularities is larger than the number of collocation points.

A Matrix Decomposition MFS Algorithm For Helmholtz Problems

Karageorghis A., Smyrlis Y. S.

Vibrations in Physical Systems

2004

Vol. 21

47--54

The Method of Fundamental Solutions (MFS) is a boundary-type method for the solution of certain elliptic boundary value problems. In this work, we develop an efficient matrix decomposition MFS algorithm for solution of exterior Helmholtz problems in domains surrounding circular domains in two dimensions. These ideas are extended for the solution of exterior Helmholtz problems in domains surrounding axisymmetric domains.