发表机构
School of Mathematical Sciences, Chongqing Normal University（重庆师范大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究二维阻抗边界腔体的弹性逆散射问题，证明形状与阻抗参数可由内曲线散射场唯一确定，并用线性采样法和最小二乘法数值重构。
AI 中文摘要
本文研究具有阻抗边界条件的二维腔体内的弹性逆散射问题。我们证明了腔体内散射场满足互易关系，并证明了腔体的形状和边界上的阻抗参数均可由在内曲线上测量的散射场唯一确定。在数值上，我们首先采用线性采样方法重构形状，然后结合位势理论与最小二乘法恢复阻抗参数。文中给出了若干数值实验，以证明我们方法的可行性和有效性。
英文摘要
In this paper, we investigate the elastic inverse scattering problem in a two-dimensional cavity with an impedance boundary condition. We prove that the scattered fields inside the cavity satisfy a reciprocity relation, and prove that both the shape of cavity and the impedance parameter on the boundary can be uniquely determined from the scattered fields measured on an interior curve. Numerically, we first employ the linear sampling method to reconstruct the shape, and then recover the impedance parameter by combining potential theory with the least squares method. Several numerical experiments are presented to demonstrate the feasibility and effectiveness of our methods.
Comments18 pages, 12 figures
