The Method of Fundamental Solutions applied to the numerical calculation of eigenfrequencies and eigenmodes for 3D simply connected domains

In this work we consider the Method of Fundamental Solutions (MFS) applied to the calculation of eigenfrequencies and eigenmodes of 3D shapes. This meshless method was considered for 2D shapes (e.g. [1], [8]) and the application to 3D simply connected domains is analysed. We propose a choice of collocation and source points in 3D adapted from the algorithm presented in [1]. An example with Dirichlet boundary conditions is considered to illustrate the convergence and the good approximations obtained with the proposed algorithm.