报告题目：Second-order flows for approaching stationary points of a class of non-convex energies via convex-splitting schemes

报 告 人：谢资清教授

报告时间：2025年4月10日下午16:20-17:20

报告地点：龙洞校区行政楼610

主 持 人：陈学松

报告摘要：The use of accelerated gradient flows is an emerging field in optimization, scientific computing and beyond. This paper contributes to the theoretical underpinnings of a recently introduced computational paradigm known as second-order flows, which demonstrate significant performance particularly for the minimization of non-convex energy functionals defined on Sobolev spaces, and are characterized by novel dissipative hyperbolic partial differential equations. Our approach hinges upon convex-splitting schemes, a tool which is not only pivotal for clarifying the well-posedness of second-order flows, but also yields a versatile array of robust numerical schemes through temporal and spatial discretization. We prove the convergence to stationary points of such schemes in the semi-discrete setting. Further, we establish their convergence to time-continuous solutions as the time-step tends to zero. Finally, these algorithms undergo thorough testing and validation in approaching stationary points of non-convex variational models in applied sciences, such as the Ginzburg-Landau energy in phase-field modeling and a specific case of the Landau-de Gennes energy of the Q-tensor model for liquid crystals.

报告人简介：谢资清，教授、博士生导师，计算与随机数学教育部重点实验室主任，湖南师范大学副校长，湘江实验室副主任，十三届全国人大代表，十四届全国政协委员。主要从事科学计算与应用数学的研究工作。现任中国高等教育学会教师教育分会副理事长、中国数学会数学教育分会常务理事兼拔尖创新人才培养小组副组长，《数学物理学报》中英文刊常务编委。博士毕业于中国科学院应用数学研究所。分别以第一完成人身份获湖南省自然科学奖一等奖和湖南省教学成果奖一等奖。入选教育部新世纪优秀人才支持计划，并获批为享受国务院政府特殊津贴专家。在SIAM J. Sci. Comput., SIAM J. Numer. Anal., Math. Comput.等期刊发表论文80余篇。主持国家自然科学基金项目9项。曾多次应邀访问美国、瑞典、挪威、德国、日本、新加坡、香港等国家和地区的知名大学，并在全球华人数学家大会、中德计算与应用数学会议等重要国际会议上做邀请报告。