Incremental proper orthogonal decomposition for PDE simulation data |
| |
Authors: | Hiba Fareed John R. Singler Yangwen Zhang Jiguang Shen |
| |
Affiliation: | 1. Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409, USA;2. School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA |
| |
Abstract: | We propose an incremental algorithm to compute the proper orthogonal decomposition (POD) of simulation data for a partial differential equation. Specifically, we modify an incremental matrix SVD algorithm of Brand to accommodate data arising from Galerkin-type simulation methods for time dependent PDEs. The algorithm is applicable to data generated by many numerical methods for PDEs, including finite element and discontinuous Galerkin methods. The algorithm initializes and efficiently updates the dominant POD eigenvalues and modes during the time stepping in a PDE solver without storing the simulation data. We prove that the algorithm without truncation updates the POD exactly. We demonstrate the effectiveness of the algorithm using finite element computations for a 1D Burgers’ equation and a 2D Navier–Stokes problem. |
| |
Keywords: | Proper orthogonal decomposition Incremental algorithm Weighted norm Finite element method |
本文献已被 ScienceDirect 等数据库收录! |
|