有界域中一类双曲型逆边值问题的数值求解研究
On the numerical solution of a hyperbolic inverse boundary value problem in bounded domains
AI总结：
针对二维有界域内嵌空腔边界重构的波动方程逆问题，结合Laguerre变换与积分方程法转化问题，提出基于正算子Fréchet导数线性化的迭代格式，结合Tikhonov正则化求解病态系统，实现了精确稳定的数值重构。
摘要：
本文研究有界域内嵌空腔的边界曲线重构逆问题，针对二维波动方程构建问题模型。研究将Laguerre变换与积分方程法结合，把逆问题转化为边界积分方程组；提出一种迭代格式，利用正算子的Fréchet导数对方程进行线性化。采用特殊求积规则后得到病态线性系统，通过Tikhonov正则化求解。数值结果表明，所提方法可实现精确且稳定的重构效果。
英文摘要：
We consider the inverse problem of reconstructing the boundary curve of a cavity embedded in a bounded domain. The problem is formulated in two dimensions for the wave equation. We combine the Laguerre transform with the integral equation method and we reduce the inverse problem to a system of boundary integral equations. We propose an iterative scheme that linearizes the equation using the Fréchet derivative of the forward operator. The application of special quadrature rules results to an ill-conditioned linear system which we solve using Tikhonov regularization. The numerical results show that the proposed method produces accurate and stable reconstructions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
