名师名家讲座: Qin Sheng 教授的学术报告
题目：A Call of Stability from a Multiscale Compact Scheme for Subwavelength Meta Optics Computation
时间：2017 年 12 月 20 日（星期三）上午 10:00-12:00
摘要：Rapid advances in subwavelength metal optics, e.g. nanophotonics, metamaterials, and plasmonics, have been demanding highly effective, efficient, and yet reliable PDE solvers. This is primarily due to broadband radiation absorptions of the metamaterials. Such optical properties are often tailorable from infrared to visible spectrums. Focusing features of the highly oscillatory beams through subwavelength metamaterials have been extremely difficult to calculate and simulate. For the simplicity, let us consider a radially symmetric electric field in transverse directions in this conversation. Thus, standard polar coordinates can be employed. To eliminate the transformation singularity occurred, we deploy a transverse domain decomposition which enables a multiscaled environmental setting that allows multi-feature wave approximations. We then consider a multiscaled compact method for a paraxial Helmholtz equation modeling nanobeams focusing through subwavelength holes. The compound numerical method is straightforward, simple-to-use. However, we can show that such a highly accurate compact scheme shies away from the stability in the conventional von Neumann sense. Can this multiscale algorithm still be vibrating in subwavelength Meta Optics applications? To this end, our investigation extends to a novel new definition of asymptotical stability. The original ideas of the consideration can be traced back to a 2007 research workshop together with Professor Shuhuang Xiang, CSU. In our study, highly oscillatory waves for subwavelength material applications are explored. Physical concerns are once again placed before traditional mathematical arguments. Intensive auxiliary expansions and analysis are carried out. It is proven that, while appropriate constraints are reinforced, the asymptotical stability of aforementioned multiscale compact method remains affective. Computational experiments with laboratorial validations will be given to illustrate our conclusions.
报告人简介：Qin Sheng 教授是美国贝勒大学数学系和物理系终身教授。Qin Sheng 教授的主要研究领域为线性和非线性偏微分方程的分裂与自适应算法及其应用，其主要研究结果在数值分析领域被誉为“Sheng-Suzuki 定理”。 Qin Sheng 教授学术造诣极深，与世界各地的知名学者有这广泛深入的合作。在二十多年的研究生涯中，Sheng 教授发表了超过 100 篇高质量论文，参与编写多部学术专著，并且为大英百科词典撰写“分裂算法”的词条。2010 年起，Qin Sheng 教授担任国际 SCI 期刊 International Journal of Computer Mathematics 主编。Qin Sheng 教授多次应邀访问美国、欧洲、拉丁美洲和中国的高校与研究机构，多次应邀参加国际数学大会并做邀请报告，多次获得美国能源部、国防部以及国家自然科学基金委的资助。目前，Qin Sheng 教授指导 3 名博士研究生和 1 名博士后研究人员。