.png){kind=icon}
返回
A model reduction method for parametric dynamical systems defined on complex geometries
.png){kind=icon}
PRE
AI
DOI：10.1016/j.jcp.2024.112923.png)
.png){kind=icon}
原文求助.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
Dynamic mode decomposition (DMD) describes the dynamical system in an equation-free manner and can be used for the prediction and control. It is an efficient data-driven method for the complex systems. In this paper, we extend DMD to the parameterized problems and propose a model reduction method based on DMD to improve the computation efficiency. This method is an offline-online mechanism. In the offline phase, we need to generate the snapshots data by solving the parameterized equations for each parameter in the training set and perform the singular value decomposition (SVD) to get the reduced operator matrices, which would lead to the substantial computation. The weighted & interpolated nearest-neighbors algorithm (wiNN) is adopted to construct the efficient surrogate models of the reduced operator matrices (including the reduced Koopman operator matrix and SVD-modes). In the online phase, for each parameter, we only need to perform the operations based on the low-dimensional matrices to get the parameter DMD solution. Moreover, we choose the least squares radial basis function finite difference method for the spatial discretization. This can make our method more applicable to the parameterized problems defined on complex geometries. At last, the reaction-diffusion, the incompressible miscible flooding and the incompressible Navier-Stokes models defined on the complex geometries are presented to illustrate the effectiveness of the proposed method.
Keyword:
Dynamic mode decomposition method
Data-driven method
Koopman operator
Weighted & interpolated nearest-neighbors
Radial basis function finite difference method
期刊
IF:
3.8
论文数:
1.6W
被引数:
7.4W
机构
引用论文
.png){kind=icon}
Local radial basis function based gridfree scheme for unsteady incompressible viscous flows基于局部径向基函数的非定常不可压缩粘性流的无网格方案
PREAI
分享收藏A LEAST SQUARES RADIAL BASIS FUNCTION FINITE DIFFERENCE METHOD WITH IMPROVED STABILITY PROPERTIES
OAAI
OAAI分享收藏
查看更多内容