应用数学青年讨论班（午餐会）—— Transformed Primal-Dual Methods for Nonlinear Partial Differential Equations
报告人：韦静蓉（UC Irvine）
时间：2023-10-18 11:45-13:30
地点：镜春园78号院77201
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：韦静蓉是加利福尼亚大学欧文分校数学系博士生，师从陈龙教授。她于2019年获得金沙娱场城app7979学士学位。她的研究兴趣主要集中在科学计算和数值分析领域，包括非线性偏微分方程、鞍点问题和约束优化算法。
讨论班简介：北京大学应用数学青年讨论班 (Applied Mathematics Seminar for Youth) 是一个由北京大学卓越研究生计划组织的学术交流平台。该讨论班定期举办一系列读书会、学术报告，涵盖广泛的应用数学领域，旨在为应用数学领域的学生提供一个互相学习、交流和探讨的机会，促进学生们在该领域的学术成长和思维能力的培养。
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