Automatic CHIEF Point Selection for Finite Element–Boundary Element Acoustic Backscattering

Abstract

Computing the backscattering of harmonic acoustic waves from underwater elastic targets of arbitrary shapes is a challenging problem of considerable practical significance. The finite element method is well suited for the discretization of the target, while the boundary element method addresses the radiation boundary condition at infinity. A disadvantage of the boundary integral method is that it yields non-unique solutions at certain wavenumbers. This failure is associated with the existence of eigensolutions of the Helmholtz equation in the interior of the complement of the fluid domain (acoustic modes). The combined Helmholtz integral equation formulation (CHIEF) credited to Schenk is employed to combine the surface Helmholtz boundary integral with equations of the interior Helmholtz relation written down at selected points within the cavity of the scatterer (i.e., in the complement of the fluid domain).The difficulty associated with this approach has always been the lack of guidance on the necessary number of interior points and on their locations. The solution to this problem proposed here is to compute the acoustic modes using the finite element method to complement of the fluid domain and to identify locations of the peaks.This novel approach aids the decision as to how many points should be employed and where they should be located. Our numerical experiments demonstrate the robustness of the proposed automatic selection of the CHIEF points’ numbers and locations.