时域电磁散射问题单轴PML方法的收敛性
Convergence of the uniaxial PML method for time-domain electromagnetic scattering problems
摘要：
本文提出并研究了求解三维时域电磁散射问题的单轴完全匹配层（PML）方法，该方法在处理各向异性散射体问题时比球面方法有很大的优势。基于拉普拉斯变换技术和能量方法，证明了截断单轴PML问题的适定性和稳定性。此外，给出了原始散射问题和截断PML问题解之间的$L^2$ -模和$L^{\infty}$ -模误差估计，从而证明了时域单轴PML方法关于PML层厚度和吸收参数的指数收敛性.证明依赖于原始散射问题和截断PML问题的EtM算子之间的误差分析，这与我们以前的工作不同（SIAM J. Numer. Anal. 58（3）（2020），1918-1940）。
英文摘要：
In this paper, we propose and study the uniaxial perfectly matched layer (PML) method for three-dimensional time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems involving anisotropic scatterers. The truncated uniaxial PML problem is proved to be well-posed and stable, based on the Laplace transform technique and the energy method. Moreover, the $L^2$-norm and $L^{\infty}$-norm error estimates in time are given between the solutions of the original scattering problem and the truncated PML problem, leading to the exponential convergence of the time-domain uniaxial PML method in terms of the thickness and absorbing parameters of the PML layer. The proof depends on the error analysis between the EtM operators for the original scattering problem and the truncated PML problem, which is different from our previous work (SIAM J. Numer. Anal. 58(3) (2020), 1918-1940).
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