参数化偏微分方程的ST-Greedy-POD降阶基方法OA

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.