“…More specifically, these equations are used to describe the Debye-Hückel equation [15], the scattering of a wave [17], the linearization of the Boltzmann equation [35], the vibration of a structure [6], the acoustic cavity problem [12], the radiation wave [19] and the steady-state heat conduction in fins [33]. In general, we assume the knowledge of the geometry of the domain of interest, the boundary conditions on the entire boundary of the solution domain and the so-called wave parameter, κ, and this gives rise to direct/forward problems for Helmholtz-type equations, which have been extensively studied both mathematically and numerically, e.g.…”