This talk is to study the convergence of the perfectly matched layer (PML) method for electromagnetic scattering problems in layered media. The PML method is widely used in the engineering literature and very efficient to solve wave scattering problems. In 2010, Chen and Zheng first proved the exponential convergence of PML method for the Helmholtz scattering problem in a two-layered medium. Since the background materials in the upper and lower half spaces are different, the Green function of the scattering problem in layered media becomes very complicated. Their proof is very technical and depends on elaborates estimates for the Green function. In this work, we develop a new framework for the exponential convergence of the PML method and for the well-posedness of the approximate problem. The methodology is used to three-dimensional electromagnetic scattering problems in two-layer media.

郑伟英，中科院数学与系统科学研究院研究员，科学与工程计算国家重点实验室副主任。1996年和1999年于郑州大学分别获学士和硕士学位，2002年于北京大学获博士学位，并获北京大学优秀博士论文。2006.10~2007.12 为慕尼黑工业大学洪堡基金访问学者。现从事有限元方法的理论与应用研究，应用领域包括非线性电磁场计算、电磁散射和磁流体力学计算等。发表学术论文30余篇，其中在SIAM系列杂志，Numer. Math.，IEEE Trans. Magn.等本领域国际核心期刊上发表论文10余篇。在大型变压器的非线性多尺度Maxwell方程、复杂界面电磁散射、原子结构计算等研究方向取得突破性成果。