论文标题
用于开放腔散射问题的自适应有限元pml方法
An adaptive finite element PML method for the open cavity scattering problems
论文作者
论文摘要
考虑一个嵌入到完美的电导导电无限地面平面中的开放腔的时间谐波平面波的电磁散射。本文涉及开放空腔散射问题的横向电和磁极的数值解。在每个极化中，使用透明的边界条件（TBC），将散射问题等效地减少到有界域中二维Helmholtz方程的边界值问题。具有完美匹配层（PML）技术的基于后验估计的自适应有限元方法是为了解决减少问题的开发。估算值遵守有限元近似误差和PML截断误差，其中后者被证明相对于PML介质参数和PML层的厚度呈指数衰减。提出了数值实验，并将两种极化的自适应有限元TBC方法与自适应有限元TBC方法进行了比较，以说明该方法的竞争行为。
Consider the electromagnetic scattering of a time-harmonic plane wave by an open cavity which is embedded in a perfectly electrically conducting infinite ground plane. This paper is concerned with the numerical solutions of the transverse electric and magnetic polarizations of the open cavity scattering problems. In each polarization, the scattering problem is reduced equivalently into a boundary value problem of the two-dimensional Helmholtz equation in a bounded domain by using the transparent boundary condition (TBC). An a posteriori estimate based adaptive finite element method with the perfectly matched layer (PML) technique is developed to solve the reduced problem. The estimate takes account both of the finite element approximation error and the PML truncation error, where the latter is shown to decay exponentially with respect to the PML medium parameter and the thickness of the PML layer. Numerical experiments are presented and compared with the adaptive finite element TBC method for both polarizations to illustrate the competitive behavior of the proposed method.
