報告題目：Transformed Primal-Dual Methods for Nonlinear Partial Differential Equations
報告人：韋靜蓉 香港中文大學
時間：2024年08月29日（星期四）4:00-4:45
地點: 正新樓209
校内聯系人：王瑞姝 wangrs_math@jlu.edu.cn
報告摘要：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).
報告人簡介：韋靜蓉香港中文大學博士後研究員。2024年畢業于加州理工大學爾灣分校，主要從事有限元方法，優化方法，非線性鞍點問題求解等領域的研究。
