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

報(bào)告人：盛秦 教授

工作單位：美國(guó)Baylor大學(xué)

時(shí)間：2017年9月29日（星期五）下午14: 30

地點(diǎn)：數(shù)學(xué)統(tǒng)計(jì)學(xué)院413會(huì)議室

報(bào)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)，英國(guó)劍橋大學(xué)獲得數(shù)學(xué)博士學(xué)位，現(xiàn)為美國(guó)Baylor大學(xué)數(shù)學(xué)系終身教授，國(guó)際計(jì)算機(jī)數(shù)學(xué)雜志《International Journal of Computer Mathematics》主編。主要從事應(yīng)用和計(jì)算數(shù)學(xué)研究，具體的研究方向包括：偏微分方程數(shù)值解法、算子分裂及區(qū)域分解法、自適應(yīng)方法、高頻振蕩問(wèn)題的數(shù)值分析、逼近論及方法、矩陣分析、計(jì)算金融、多物理場(chǎng)應(yīng)用、并行計(jì)算、以工程應(yīng)用為目標(biāo)的軟件設(shè)計(jì)等。出版學(xué)術(shù)專(zhuān)著6部，發(fā)表學(xué)術(shù)論文100余篇。

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                                                寧夏大學(xué)數(shù)學(xué)統(tǒng)計(jì)學(xué)院

                                                    2017年9月27日