报告题目：Transformed Primal-Dual Methods for Nonlinear Partial Differential Equations
报告人：韦静蓉 香港中文大学
时间：2024年08月29日（星期四）4:00-4:45
地点: 正新楼209
校内联系人：王瑞姝 wangrs_math@jlu.edu.cn
报告摘要：Steady-state nonlinear partial differential equations can be understood as finding the minimum of some smooth convex energy with equality constraints. After introducing the Lagrange multiplier, we are seeking the saddle point of a nonlinear system. A transformed primal-dual (TPD) flow is developed for such a nonlinear saddle point system. The flow for the dual variable contains a Schur complement which is strongly convex. Exponential stability of the saddle point is obtained by showing the strong Lyapunov property. A TPD iteration is derived by time discretization of the TPD flow. Under mild assumption, the algorithm is global linearly convergent, and the convergence rate depends on the relative condition number of the objective function and the Schur complement under variant metric as preconditioners. The developed algorithm is then applied to partial differential equations: Darcy–Forchheimer model and a nonlinear electromagnetic model. Numerical results demonstrate the efficiency of the method. This is joint work with Long Chen (UC Irvine) and Ruchi Guo (CUHK).
报告人简介：韦静蓉香港中文大学博士后研究员。2024年毕业于加州理工大学尔湾分校，主要从事有限元方法，优化方法，非线性鞍点问题求解等领域的研究。
