Second-order flows for solving non-convex variational problems
数学专题报告
报告题目(Title)：Second-order flows for solving non-convex variational problems
报告人(Speaker)：刘伟（国防科技大学）
地点(Place)：后主楼1124
时间(Time)：3月22日（星期六），10:00am-11:00am
邀请人(Inviter)：蔡勇勇
报告摘要
In this talk, we introduce a novel computational model based on the second-order flows (i.e., a class of dissipative second-order hyperbolic PDEs) for solutions of non-convex variational problems with possible constraint. We explore both the theoretical and numerical aspects of second-order flows and highlight several challenges in analysis and applications. Specifically, efficient second-order flow approaches are developed to address the minimization of the Gross-Pitaevskii energy functional under the mass normalization constraint to compute ground states of rotating Bose-Einstein condensates. Extensive numerical results demonstrate the superiority of second-order flow methods over the commonly used gradient flow methods. Furthermore, the convergence of second-order flows to stationary points is established for a wide class of unconstrained non-convex variational problems through convex-splitting schemes, and typical applications such as the minimization of Ginzburg-Landau energy in phase-field modelings and Landau-de Gennes energy in the Q-tensor model for liquid crystals are explored.
主讲人简介
刘伟，国防科技大学理学院数学系副教授。主要从事非线性偏微分方程数值方法及其在量子物理学中的应用研究，包括非线性薛定谔方程相关计算方法、玻色-爱因斯坦凝聚体基态和激发态的高效算法，以及非线性偏微分方程多鞍点解的新型计算方法等方面。研究成果发表在SIAM J. Sci. Comput.、J. Comput. Phys.、Math. Models Methods Appl. Sci.、Sci. China Math.等著名期刊上。主持国家自然科学基金青年科学基金项目1项和省部级科研项目1项。曾获全国“博士后国际交流计划”派出项目资助（2021），以及湖南省优秀博士学位论文（2022）、湖南省计算数学应用软件学会一等青年优秀论文（2022）等奖励。
