期刊
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
卷 322, 期 -, 页码 483-514出版社
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2017.04.033
关键词
RPM; Nonlinear model reduction; PGD; Reduced basis; LATIN method; Hyperreduction
资金
- French Agence Nationale pour la Recherche through the SIM-DREAM project [ANR-10-COSI-0006]
- Agence Nationale de la Recherche (ANR) [ANR-10-COSI-0006] Funding Source: Agence Nationale de la Recherche (ANR)
A new approximation technique, called Reference Point Method (RPM), is proposed in order to reduce the computational complexity of algebraic operations for constructing reduced-order models in the case of time dependent and/or parametrized nonlinear partial differential equations. Even though model reduction techniques enable one to decrease the dimension of the initial problem in the sense that far fewer degrees of freedom are needed to represent the solution, the complexity of evaluating the nonlinear terms and assembling the low dimensional operator associated with the reduced-order model still scales with the size of the original high-dimensional model. This point can be critical, especially when the reduced-order basis changes throughout the solution strategy as it is the case for model reduction techniques based on Proper Generalized Decomposition (PGD). Based on the concept of spatial, parameter/time reference points and influence patches, the RPM defines a compressed version of the data from which an approximate low-rank separated representation by patch of the operators can be constructed by explicit formulas at low-cost without resorting to SVD-based techniques. An application of the RPM to PGD-based model reduction for a nonlinear parametrized elliptic PDE previously studied by other authors with reduced-basis method and EIM is proposed. It is shown that computational complexity to construct the reduced-order model can be divided in practice by one order of magnitude compared with the classical PGD approach. (C) 2017 Elsevier B.V. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据