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Numerical calculation of eigensolutions of 3D shapes using the Method of Fundamental Solutions

Antunes, Pedro R. S.

Numerical Methods for Partial Differential Equations, 27 (2011), 1525-1550

In this work, we study the application of the Method of Fundamental Solutions (MFS) for the calculation of eigenfrequencies and eigenmodes in two and three-dimensional domains. We address some mathematical results about properties of the single layer operator related to the eigenfrequencies. Moreover, we propose algorithms for the distribution of the collocation and source points of the MFS in three-dimensional domains which is an extension of the choices considered by Alves and Antunes (CMC 2(2005), 251–266) for the two-dimensional case. Also the application of the Plane Waves Method is investigated. Several examples with Dirichlet and Neumann boundary conditions are considered to illustrate the performance of the proposed methods.