The Method of Fundamental Solutions applied to the calculation of eigenfrequencies and eigenmodes of 2D simply connected shapes

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 problems. This meshless method was already applied to simple geometry domains with Dirichlet boundary conditions (cf. Karageorghis (2001)) and to multiply connected domains (cf. Chen, Chang, Chen, and Chen (2005)). Here we show that a particular choice of point-sources can lead to very good results for a fairly general type of domains. Simulations with Neumann boundary condition are also considered.