A Meshless Method for the Helmholtz Eigenvalue Problem Based on the Taylor Series of the 3-D Green's Function

The solution of the Helmholtz eigenvalue problem is considered through the use of the method of the fundamental solutions. Taylor series of these solutions are employed to form a polynomial eigenvalue problem. The presented method diff ers from other methods such as the multiple reciprocity method. Here, the Green's function itself is expanded and no integration is performed. Results on classical geometries (sphere, parallelepiped box and finite cylinder) demonstrate the accuracy of the method for the determination of the eigenvalues with Neumann, Dirichlet and Robin boundary conditions. Furthermore, the center of the Taylor approximation is shown to be adjustable, allowing the method to be theoretically eff ective for any arbitrarily part of the eigenvalue spectra.