Computing Highly Oscillatory Problems Faster and More Accurately

报告摘要：

Fast and accurate computations of optical wave devices such as waveguides and couplers have been crucial to the development of light integrated systems. Core parts of such calculations often involve advanced computational procedures for investigating the wave propagation characteristics via highly oscillatory differential equations of integrals. While the beam propagation method, which is based on fast Fourier transforms, has been popular in the study, different decomposition schemes and  Filon Type methods  are also introduced to the research. To improve the accuracy of a numerical method used, a traditional approach is to increase the density of the grid or decrease the mesh step sizes utilized. With a uniform mesh and step size, the cost for doing so may quickly become prohibitive if a high wave frequency is encountered. Non-uniform mesh structures and step sizes, on the other hand, may offer certain advantages in the situation. However, they are often cumbersome to implement in industrial applications. This talk will introduce a number of the latest approaches in the area for highly accurate, yet rapid numerical methods for solving paraxial, or parabolic, wave equations in order to separate inaccuracies inherent in numerical methods from inaccuracies due to paraxial waves. This talk will be suitable for all graduate and senior undergraduate students.

报告人简介： 盛秦 (Qin Sheng) 教授，于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，具体的研究方向涉及：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、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。发表学术专著及论文100余篇。现任美国国家科研基金会 Penal Member。