Time-Harmonic Acoustic Scattering from Locally Perturbed Half-Planes

Abstract

This paper is concerned with time-harmonic acoustic scattering of plane waves in one or two inhomogeneous half-planes with an unbounded interface. The contrast function is supposed to have a compact support, while the infinite interface is a local perturbation of the x 1 -axis. For an acoustically impenetrable interface, the scattering phenomenon occurs in one half-plane only and the impedance (Robin) boundary value problem is investigated. In the penetrable case, we study a transmission problem in two half-planes. Our approach for forward scattering is based on the finite element method in a truncated bounded domain coupled with the boundary element method. Numerical experiments are tested to verify our scheme. For the inverse problem, we prove that the near-field data of a finite number of incoming plane waves or a single point source wave uniquely determine the shape of a rectangular cavity of impedance-type.

Time-Harmonic Acoustic Scattering from a Nonlocally Perturbed Trapezoidal Surface

“…Remark 2.3 (i) Obviously, the definition of our outgoing radiation condition depends on the incident angle θ and the height h of the scattering surface Γ in the vertical direction. If h = 0 (i.e., Γ is a local perturbation of the original straight line {x 1 = 0}), then we see u tot L = u tot R and thus the proposed radiation condition could be reduced to the usual condition for scattering problems in a locally-perturbed half-plane (see e.g., [1,2,24,28,39,40]). Moreover, we remark that u − u in still satisfies the Angular Spectrum Representation (1.6) for general rough surface problems.…”

“…For instances, if a bounded obstacle is embedded into a homogeneous background medium, the scattered wave is purely outgoing at infinity and satisfies the classic Sommerfeld radiation condition (SRC) [17]. When the structure is filled in by a two-layered medium with a locally perturbed planar surface, the perturbed wave field due to the local perturbation, is outgoing at infinity and satisfies the SRC [36,13,2,28]; see also [1,40,24,39] for studies on impenetrable locally perturbed surfaces. However, in the case of a globally perturbed rough surface, by which we mean a non-local perturbation of a planar surface such that the surface lies within a finite distance of the original plane, one in general cannot explicitly extract an outgoing wave from the scattered wave to meet the SRC.…”

“…[9,18]). If Γ is a local perturbation of the original straight line {x 2 = 0} , it was proved in a series of papers (see [1,2,24,28,39,40]) that u sc can be decomposed into two parts:…”

A Numerical Mode Matching Method for Wave Scattering in a Layered Medium with a Stratified Inhomogeneity

“…eq:sol:para eq:sol:para According to [25,8,1], we have the following existence and uniqueness results:…”

A Novel Integral Equation for Scattering by Locally Rough Surfaces and Application to the Inverse Problem: The Neumann Case

“…A symmetric coupling method of finite element and boundary integral equations wasn developed in [2], which can be applied to arbitrarily shaped and filled cavities with Neumann or Dirichlet boundary conditions. Recently, in [3], the scattering problem by a locally perturbed interface is studied by a variational method coupled with a boundary integral equation method and numerically solved, based on the finite element method in a truncated bounded domain coupled with the boundary element method. It should be mentioned that some studies related to the scattering problem (1.1)-(1.3) have also been conducted extensively.…”