报告题目：A NGO-based numerical scheme for Maxwell-Bloch system

报 告 人：王汉权教授（云南财经大学）

报告时间：2022年12月8日  15:30

报告地点：腾讯会议（362206288）

报告摘要：

We consider an electromagnetic field from Laser in interaction with a quantized medium. The quantization of the medium is necessary in order to correctly describe laser pulse absorption and amplification as the classical physical theory cannot be used for that. The mathematical model used here is the semi- classical Maxwell-Bloch (MB) system. It is esentially a multi-scale problem. Mathematical analysis and computation of semi-classical MB system is very helpful for studying various kinds of physical phenomena appeared in the making of quantum cascade Laser, quantum dot Laser .....However, the model is singular. Solving it directly either numerically or analytically is quite difcult. Previously, researchers used various approximation methods such as slowly varying envelope approximation or reductive multi-scale method to reduce the MB system to simplified models such as NLSE, KDV or m-KD.....These works are very helpful but not directly. In this talk, inspired from S. Jin and his coauthors’recent work, we conduct a nonlinear geometric optics (NGO) based numerical scheme to solve the semi-classical MB system directly. Algorithm and Analysis on how the scheme can be workable are provided. The method presented here may be useful for solving many other similar types of singular PDEs as well.

报告人简介：

王汉权博士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数学专业硕士生导师、统计学专业博士生导师、云南财经大学学术委员、中国工业与应用数学学会会员、中国计算数学学会理事等。2020起兼任四川大学数学专业博士生导师。

研究领域涉及计算数学与科学工程计算，各种偏微分方程、随机偏微分方程的数值解法（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。当前的研究兴趣为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等方面中的应用。已主持完成三项国家自然科学基金，一项教育部“留学回国人员科研启动基金”、一项云南省教育厅科学研究重点项目及多项省部级项目基金。已在《SIAM Joumal of Numerical Analysis》《SIAM Journal on Applied Mathematics》《Journal of Computational Physics》《Journal of Scientific Computing》等杂志发表SCI检索论文三十余篇，并在科学出版社出版专著一部，论文被引800余次。于2013年入选教育部新世纪优秀人才支持计划，2014年获得“云南省有突出贡献优秀专业技术人才”称号，2017年获得云南省自然科学奖三等奖一项。