报告题目：A spectral element method and its application to compute the nonlinear optical waveguide
报 告 人：王汉权 教授 云南财经大学
报告时间：2021年11月16日 10:00-11:00
报告地点：腾讯会议ID：138 662 333 会议密码：1116
校内联系人：许志国 xuzg2014@jlu.edu.cn
报告摘要：Computation of nonlinear optical waveguide needs to solve nonlinear eigenvalue/eigenfunctionproblem mathematically. However, usually the refractive index in the nonlinear optical waveguide are discontinuous, which makes solution of nonlinear eigenvalue/eigenfunction problem not smooth enough. In this work, we mainly discuss how to use high-order spectral element method (SEM) to discretize such problem and propose an iterative algorithm for computing nonlinear optical waveguide problems with discontinuous refractive index profiles. Starting from the linear eigenvalue/eigenfunction problem, we adopt SEM to discretize them and solve the resulting discretized system with Matlab eigen solver; For the nonlinear problem, we first change the nonlinear problem into a corresponding linear problem, and then solve the nonlinear problem by usage of the iterative method. The proposed method has advantage of high-order accuracy and lower-order cost. The accuracy and efficiency of the method are tested by several one-dimensional and two-dimensional linear optical waveguide structures with exact or approximate solutions. Numerical results for some one-dimensional and two-dimensional nonlinear optical waveguide structure are presented.
报告人简介：王汉权，现任云南财经大学特聘教授、云南财经大学统计与数学学院副院长、博士生导师。2013获得教育部新世纪优秀人才基金资助。2014年获得“云南省有突出贡献优秀专业技术人才”称号。2017年获得“云南省中青年学术带头人”称号。曾经前往新加坡国立大学、香港科技大学、美国纽约哥伦比亚大学等大学做访问学者。主要从事计算数学与科学工程计算，感兴趣的研究领域包括：计算数学及其在玻色-爱因斯坦凝聚态物理、材料中的晶体位错现象、基本物质（原子、分子、等离子体等）在强激光场下的物理性质与反应、金融数学等方面中的应用。已经从事科学研究的领域包括计算数学与科学工程计算，偏微分方程数值解法（有限差分法、谱方法、谱元法等）的设计与应用，泛函极值问题求解方法设计与应用，最优化理论方法与应用，计算机模拟玻色-爱因斯坦凝聚态中的涡旋现象和材料科学中的晶体位错现象。主持完成国家自科基金项目三项，目前主持国家自科基金面上项目一项。
