2019/06/24 by Xiaoying Dai, Xiong Kuang, Dai, Xiaoying +5
Chemistry · Computer Science · Decision Sciences · Engineering · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Chemistry #Computational Fluid Dynamics and Aerodynamics #Computer science #Decomposition #Geometry #Grid #Mathematical analysis #Mathematical optimization #Mathematics #Mechanics #Model Reduction and Neural Networks #Partial differential equation #Physics #Probabilistic and Robust Engineering Design #Proper orthogonal decomposition #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.1906.09736
published in arXiv (Cornell University) (Cornell University) · 28 pages, 6 figures, 13 tables
openalex publication_date 2019/06/24 · openalex created_date 2019/06/27 · arxiv created 2020/07/23 · arxiv updated 2020/07/24 · openalex updated_date 2026/07/28
In this article, we propose a two-grid based adaptive proper orthogonal decomposition (POD) method to solve the time dependent partial differential equations. Based on the error obtained in the coarse grid, we propose an error indicator for the numerical solution obtained in the fine grid. Our new algorithm is cheap and easy to be implement. We apply our new method to the solution of time-dependent advection-diffusion equations with the Kolmogorov flow and the ABC flow. The numerical results show that our method is more efficient than the existing POD methods.