论文标题
麦克斯韦方程的时间域PML问题分析波导
Analysis of the time-domain PML problem for Maxwell's equations in a waveguide
论文作者
论文摘要
本文涉及无限矩形波导中时间域电磁散射问题的数学分析。开发了透明的边界条件，以将问题重新制定为有限域中等效的初始边界价值问题。对于减少的问题，获得了良好的稳定性和稳定性。研究了完美匹配的层方法以截断波导。结果表明，截短的问题达到了独特的解决方案。此外，在原始散射问题的解决方案和截断问题之间给出了明确的误差估计。基于估计值，为截断问题建立了稳定性和指数收敛。对于误差，实现了最佳界限，并明确依赖于完美匹配的层的参数。
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.
