波导中Maxwell方程的时域PML问题分析
Analysis of the time-domain PML problem for Maxwell's equations in a waveguide
摘要：
本文对无限长矩形波导中的时域电磁散射问题进行了数学分析。通过引入透明边界条件，将问题转化为有界区域上的等价初边值问题。得到了约化问题的适定性和稳定性。研究了完全匹配层法截断波导的方法。它表明，截断问题达到一个唯一的解决方案。此外，给出了原始散射问题的解与截断问题的解之间的显式误差估计。在此基础上，证明了截断问题的稳定性和指数收敛性。最佳界实现的误差与完全匹配层的参数的显式依赖。
英文摘要：
This paper is concerned with the mathematical analysis of the time-domain electromagnetic scattering problem in an infinite rectangular waveguide. A transparent boundary condition is developed to reformulate the problem into an equivalent initial boundary value problem in a bounded domain. The well-posedness and stability are obtained for the reduced problem. The perfectly matched layer method is studied to truncate the waveguide. It is shown that the truncated problem attains a unique solution. Moreover, an explicit error estimate is given between the solutions of the original scattering problem and the truncated problem. Based on the estimate, the stability and exponential convergence are established for the truncated problem. The optimal bound is achieved for the error with explicit dependence on the parameters of the perfectly matched layer.
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