【学术预告】Time-parallel time-integration schemes for ordinary and partial differential equations​

报告题目：Time-parallel time-integration schemes for ordinary and partial differential equations

报 告 人：李世顺

报告时间：2023年3月2日（周四）15:00-17:00

报告地点：数学楼315会议室

报告摘要：In this talk, we first introduce some space-time domain decomposition methods for solving parabolic equations discretized by the backward Euler and BDF2 schemes in time and finite elements in space. Then we present some new time integration schemes, the block implicit methods (BIM), for ordinary and partial differential equations. The advantages of BIM are that they possess favorable stability properties, offer high order of accuracy and have no start-up issues. We also construct a new type of special BIM defined by a positive definite matrix and a positive diagonal matrix. It shows that the traditional finite element theory for parabolic problems discretized by the backward Euler schemes can also be extended to BIM. Finally, some numerical results are also reported to show the effectiveness of BIM.

报告人简介：李世顺，河南理工大学副教授。2011年博士毕业于浙江大学数学系。2013年-2014年美国科罗拉多大学计算机系博士后，2018年1月-2018年12月中国科学院深圳先进技术研究院访问学者。2020年7月-2020年12月澳门大学访问学者。研究方向为求解偏微分方程的区域分解方法和并行算法。目前主要研究时空并行区域分解算法的理论与应用。相关成果发表在SIAM J. Sci. Comput.，SIAM J. Numer. Anal.，Numer. Linear Algebra Appl.和Appl. Numer. Math.等期刊上。