题 目：On Numerical Stabilities of a Decomposed Compact Method for Highly Oscillatory Nanophotonical and Metamaterials Applications

报告人：盛秦 教授

工作单位：美国Baylor大学

时间：2017年9月29日（星期五）下午14: 30

地点：数学统计学院413会议室

报告摘要：

Recent advances in subwavelength metal optics, e.g. nanophotonics, metamaterials, and plasmonics, provide several new examples where nanostructured metals perform the separate tasks of absorption and charge separation necessary for solar power conversion. Nanostructured metals are extremely efficient broadband absorbers of radiation, with tailorable optical properties throughout the visible and infrared spectrum. This discussion concerns numerical stabilities of a decomposed compact finite difference method for solving Helmholtz partial differential equations in subwavelength metal optics computations. Radially symmetric electric fields in transverse directions are assumed. A higher accuracy in transverse approximations for nanostructured performance simulations is particularly interested in our investigations. To this end, intensive auxiliary expansions are carried out. Standard polar coordinates are utilized, and a decomposition strategy is applied to remove the anticipated singularity. It is proven that, while the highly accurate compact algorithm shies away from the stability in the conventional von Neumann sense, it is asymptotically stable with index one. Computational experiments are provided to illustrate our conclusions.

盛秦(Sheng Qin)，英国剑桥大学获得数学博士学位，现为美国Baylor大学数学系终身教授，国际计算机数学杂志《International Journal of Computer Mathematics》主编。主要从事应用和计算数学研究，具体的研究方向包括：偏微分方程数值解法、算子分裂及区域分解法、自适应方法、高频振荡问题的数值分析、逼近论及方法、矩阵分析、计算金融、多物理场应用、并行计算、以工程应用为目标的软件设计等。出版学术专著6部，发表学术论文100余篇。

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