报告题目：Numerical methods for the Klein-Gordon-Dirac system in thenonrelativistic limit regime

报 告 人：易雯帆（湖南大学）

报告时间：2021年8月25日  15:00-16:30

报告地点：数学研究中心报告厅

报告摘要：

In the nonrelativistic limit regime, fhe KGD system admits rapid oseillations in time as a small dimensionless parameter tends to cero. The temporal oscillatory structure of the solution causes severe numerical burdens in practical computations. Even for the stablenumerical approximations, they may come out completely wrong unless the temporal oscillation is completely resolved with sefficiently small mesh size which depends greatly on the small parameter.  In addition, the nonlinear Yukawa interaction and the indefinite Diracoperator bring other significant difficulties. Several  numerical miethods are presented for discretizing the massive Klein-Gordon-Dirac(KGD) system in the nonrelativistic limit regime. Rigorous error estimates are established for the numerical methods by focusing on how the errors depend explicitly on the small parameter in addition to the time step and mesh size. Then uniformly accurate numerical schemes are considered and analyzed.

报告人简介：

易雯帆，湖南大学数学学院助理教授，硕士生导师。2016年获湖南师范大学计算数学博士学位，2016-2018年在北京计算科学研究中心从事博士后研究，期间访问新加坡国立大学数学系一年，2018年入职湖南大学。主要从事科学与工程计算及应用数学方面的研究。研究工作涉及非线性偏微分方程多解计算大范围收敛性算法及量子力学多尺度高震荡模型的高效数值方法分析及敷值模拟等方面的研究。在Multiscale Model. Simul., IMA J.Numer. Anal., Common. Math. Sci., J. Sci. Comput., J. Comput. Appl. Math.等杂志上发表文章多篇，现主特国家自然科学基金青年项目1项。