报告题目：Implicit-explicit relaxation Runge-Kutta methods: construction, analysis and applications to PDEs

报告人：李东方教授 华中科技大学

报告时间：2022年6月20日14:30-16:30

报告地点：腾讯会议404 521 689

报告摘要：Spatial discretizations of time-dependent partial differential equations usually result in a large system of semi-linear and stiff ordinary differential equations. Taking the structures into account, we develop a family of linearly implicit and high order accurate schemes for the time discretization, using the idea of implicit-explicit Runge-Kutta methods and the relaxation techniques. The proposed schemes are monotonicity preserving/conservative for the original problems, while the previous linearized methods are usually not. We also discuss the linear stability and strong stability preserving (SSP) property of the new relaxation methods. Numerical experiments on several typical models are presented to confirm the effectiveness of the proposed methods.

李东方，华中科技大学数学与统计学院教授，博导，中国系统仿真学会仿真算法专业委员会委员。曾先后赴加拿大McGill大学，香港城市大学从事博士后研究。主要研究微分方程数值解、系统仿真和信号处理等领域，在微分方程保结构算法和分数阶微分方程的高效数值算法和理论上取得一些有意义的进展。主要工作发表在《SIAM. J. Numer. Anal.》，《SIAM. J. Sci. Comput.》、《Math. Comput》《J. Comp. Phys.》等多个国际著名计算学科SCI期刊上，多篇为高被引论文。