A non-iterative sampling method for inverse elastic wave scattering by rough surfaces

Elastic scattering from rough surfaces in three dimensions

Consider the elastic scattering of a plane or point incident wave by an unbounded and rigid rough surface. The angular spectrum representation (ASR) for the time-harmonic Navier equation is derived in three dimensions. The ASR is utilized as a radiation condition to the elastic rough surface scattering problem. The uniqueness is proved through a Rellich-type identity for surfaces given by uniformly Lipschitz functions. In the case of flat surfaces with a local perturbation, we deduce an equivalent variational formulation in a truncated bounded domain and show the existence results for general …

三维中无界确定性与随机粗糙面的时谐弹性散射

Time-harmonic elastic scattering by unbounded deterministic and random rough surfaces in three dimensions

该研究通过变分方法分析三维无界刚性粗糙面弹性波时谐散射的适定性，证明了确定性情形的稳定性估计及显式先验界，并拓展得到随机表面散射解的同类界。

局部粗糙界面的弹性散射

Elastic scattering by locally rough interfaces

本文通过发现应力向量的基本恒等式，推导出弹性散射中粗糙界面的适定性结果，首次证明了直接问题的唯一性和双层格林张量的存在性。

A priori bounds for elastic scattering by deterministic and random unbounded rough surfaces

This paper investigates the elastic scattering by unbounded deterministic and random rough surfaces, which both are assumed to be graphs of Lipschitz continuous functions. For the deterministic case, an a priori bound explicitly dependent on frequencies is derived by the variational approach. For the scattering by random rough surfaces with a random source, well-posedness of the corresponding variation problem is proved. Moreover, a similar bound with explicit dependence on frequencies for the random case is also established based upon the deterministic result, Pettis measurability theorem and…

Analysis of a time-dependent fluid-solid interaction problem above a local rough surface

This paper is concerned with the mathematical analysis of time-dependent fluid-solid interaction problem associated with a bounded elastic body immersed in a homogeneous air or fluid above a local rough surface. We reformulate the unbounded scattering problem into an equivalent initial-boundary value problem defined in a bounded domain by proposing a transparent boundary condition (TBC) on a hemisphere. Analyzing the reduced problem with Lax-Milgram lemma and abstract inversion theorem of Laplace transform, we prove the well-posedness and stability for the reduced problem. Moreover, an a prior…

Convergence of the perfectly matched layer method for transient acoustic-elastic interaction above an unbounded rough surface

This paper is concerned with the time-dependent acoustic-elastic interaction problem associated with a bounded elastic body immersed in a homogeneous air or fluid above an unbounded rough surface. The well-posedness and stability of the problem are first established by using the Laplace transform and the energy method. A perfectly matched layer (PML) is then introduced to truncate the interaction problem above a finite layer containing the elastic body, leading to a PML problem in a finite strip domain. We further establish the existence, uniqueness and stability estimate of solutions to the P…