Modified 2.5D singular boundary methods to deal with spurious eigensolutions in exterior acoustic problems

Abstract

This paper studies the problem of spurious eigensolutions in the context of the singular boundary method (SBM) formulated in the two-and-a-half-dimensional (2.5D) domain and proposes two numerical schemes to overcome this numerical difficulty. The SBM can be seen as a version of the method of fundamental solutions where the source points are located at the physical boundary. Similar to other boundary-type discretization schemes, the SBM also encounters the non-uniqueness problem at the vicinity of the eigensolutions of the corresponding interior problem. In the 2.5D domain framework, the so-called fictitious eigenfrequencies appearing in 3D problems arise in the form of spurious dispersion curves associated with propagation modes of the corresponding interior problem. The two enhanced 2.5D SBM approaches proposed in this work, based on the Burton–Miller method in one case and the dual surface method in the other, are designed to filter out the spurious eigenvalues from the simulation results and deliver accurate solutions along the wavenumber-frequency spectrum. Three benchmark examples including the radiation problems of an infinitely long cylinder under Dirichlet and Neumann boundary conditions and the radiation problem of a longitudinally infinite object with a constant star-like cross section subjected to a Dirichlet boundary condition are considered to study the proposed methods. The results demonstrate the capability of the proposed numerical schemes to successfully avoid the non-uniqueness problem when the 2.5D SBM is employed.