报 告 人:程青 博士
报告题目:Constructing structure-preserving schemes via Lagrange multiplier approach
报告时间:2022年12月03日 上午10:00-11:00
报告地点:腾讯会议 ID:893-109-196
主办单位:数学与统计学院、科学技术研究院
报告人简介:
程青博士,2018年博士毕业于厦门大学,2019年至2021年在美国伊利诺伊理工大学任职访问助理教授,2021年至今在美国普渡大学任职访问助理教授,在SIAM J. Numer. Anal., SIAM J. Sci. Comput., Comput. Methods Appl. Mech. Eng., J. Comput. Phys.等国际著名杂志发表论文十余篇。其中发表于SIAM J. Sci. Comput. 和J. Sci. Comput.两篇论文入选ESI高被引文章。论文的引用者包括多位美国科学院院士,比如Stanely Osher教授,以及多位国际数学家大会报告人,SIAM fellow,AMS fellow。由于这些工作,程青博士多次受邀在SIAM年会,A3(China-Japan-Korea)Workshop等国际会议、研讨会做邀请报告。程青博士长期担任SIAM J. Math. Anal.; J. Comput. Phys.; Commun. Comput. Phys.; J. Sci. Comput.等杂志的审稿人。
报告摘要:
In the talk, I will introduce a new Lagrange multiplier approach to construct efficient and accurate structure-preserving schemes for a class of semi-linear and quasi- linear parabolic equations. To be more specific, I will introduce how to construct positivity/bound-preserving, length-preserving, energy-dissipative schemes for a large class of PDEs. I will establish stability results under a general setting, and carry out an error analysis for second-order structure-preserving schemes. Finally, I will apply our approach to several typical PDEs which preserve structures described above. Some numerical results will be presented to validate our approach.