新疆大学学报（自然科学版中英文）2026，Vol.43Issue(3)：285-294,10.DOI:10.13568/j.cnki.651094.651316.2025.10.04.0002
参数化偏微分方程的ST-Greedy-POD降阶基方法
ST-Greedy-POD Reduced Basis Method for Parameterized Partial Differential Equations
摘要
Abstract
Many engineering problems require simulations of parameterized partial differential equations.It takes a lot of time to solve this kind of problem when the discretization scale of the equation is larger and the parameter space is more com-plex.To improve the solving efficiency of partial differential equations with parameters,this paper proposes an ST-Greedy-POD reduced basis method for parameterized PDEs based on the space-time finite element discretization.Firstly,the param-eterized PDE is discretized in both space and time via the space-time finite element method,yielding a parameterized alge-braic equation.Then,the parameterized equation is separated into the parameter-dependent part and the parameter-independent part.Secondly,the Greedy algorithm is adopted to select optimal parameters from the parameter sample set ac-cording to posterior error,and the space-time reduced basis space is constructed iteratively,to further derive the space-time projection matrix.Finally,the parameterized system separated by parameters is projected onto the space-time reduced basis matrix to obtain the space-time parameterized reduced-order model and the corresponding reduced basis algorithm is pre-sented.The proposed method reduces both the time variable and the space variable simultaneously.The results of two numeri-cal examples verify the feasibility and effectiveness of the proposed method.关键词
参数化偏微分方程/时空有限元/降阶基空间/ST-Greedy-POD降阶基Key words
parameterized partial differential equations/space-time finite element/reduced basis space/ST-Greedy-POD re-duced basis分类
数理科学引用本文复制引用
王丽,王兆鸿,蒋耀林..参数化偏微分方程的ST-Greedy-POD降阶基方法[J].新疆大学学报（自然科学版中英文）,2026,43(3):285-294,10.基金项目
新疆维吾尔自治区自然科学基金"基于离散正交多项式的模型降阶方法研究"(2023D01C163),"大规模复杂系统的最优化模型降阶方法研究"(2025D01C278) （2023D01C163）
新疆维吾尔自治区"天池英才"引进计划项目"离散控制系统的正交分解模型降阶方法研究". （）
