报告题目 (Title)：Applications of Proper Orthogonal Decomposition Extrapolation Methods（适当正交分解外推方法的应用）
报告人 (Speaker)：李宏 教授（内蒙古大学）
报告时间 (Time)：2026年5月18日(周一) 15:00
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：盛万成
主办部门：理学院数学系
报告摘要：The applications of proper orthogonal decomposition (POD) extrapolation methods for numerically solving partial differential equations are discussed in the presentation. The core strategy constructs a low-dimensional POD basis from a few full-order solution snapshots on a short initial interval [0,T_0] (T_0\ll T), then extrapolates reduced-order solutions on [T_0,T] to avoid redundant computations. The reduced order method based on POD techniques, for example, the reduced order FEM for Burgers equation (coefficient vector reduction)，POD-TDG-STFE for parabolic problems (space-time reduction with Radau quadrature), ROLGE for the Allen-Cahn equation, and ROLGE for the Cahn-Hilliard equation (both using SAV approaches with Legendre-Galerkin discretization). Across all methods, the error has a unified structure--classical discretization error plus a POD truncation term controlled by the number of basis functions $d$. Computational speedup ranges from $3\times$ to over $40\times$ with only $d=2$--$15$ basis functions, while preserving key properties such as energy stability for phase field models
