Construction and Numerical Assessment of Local Absorbing Boundary Conditions for Heterogeneous Time-Harmonic Acoustic Problems

Abstract

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TRAC method in dissipative media—a first analysis in frequency domain and homogeneous media

“…Moreover, the ABC actually depends on the model as well. Therefore, many types of ABCs have been designed for the acoustic waves in the case of heterogeneous media [29,33] and multiple scattering [34][35][36]. Then, for the Maxwell equations, non-reflecting boundary conditions are proposed in [37][38][39], and for the elastic waves see [40][41][42][43].…”

Low-order Prandtl-Glauert-Lorentz based Absorbing Boundary Conditions for solving the convected Helmholtz equation with Discontinuous Galerkin methods

“…Following the original idea of [HHT03], complete absorbing (or radiation) boundary conditions have been proposed in [Kim14] for the case of the convected Helmholtz equation with a uniform flow in a waveguide. Very recently, radiation boundary conditions have been constructed by applying a micro-local factorization of the convected Helmholtz operator when the flow is aligned with a coordinate axis [MAGB21]. The construction of an exact ABC is also feasible from a theoretical point of view but it involves a non-local operator whose discretization induces an additional computational load.…”