期刊
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
卷 80, 期 8, 页码 1025-1057出版社
WILEY-BLACKWELL
DOI: 10.1002/nme.2540
关键词
metamodel; surrogate; reduced-order model (ROM); physics-based model; parameterized partial differential equation (PDE); radial basis functions (RBF); proper orthogonal decomposition (POD); design optimization; fluid dynamics problems
资金
- Agence Nationale de la Recherche ANR RNTL
This paper presents a methodology for constructing low-order surrogate models of finite element/finite volume discrete solutions of parameterized steady-state partial differential equations. The construction of proper orthogonal decomposition modes in both physical space and parameter space allows us to represent high-dimensional discrete solutions using only a few coefficients. An incremental greedy approach is developed for efficiently tackling problems with high-dimensional parameter spaces. For numerical experiments and validation, several non-linear steady-state convection-diffusion-reaction problems are considered: first in one spatial dimension with two parameters, and then in two spatial dimensions with two and five parameters. In the two-dimensional spatial case with two parameters, it is shown that a 7 x 7 coefficient matrix is sufficient to accurately reproduce the expected solution, while in the five parameters problem, a 13 x 6 coefficient matrix is shown to reproduce the Solution with sufficient accuracy. The proposed methodology is expected to find applications to parameter variation Studies, uncertainty analysis, inverse problems and optimal design. Copyright (c) 2009 John Wiley & Sons, Ltd.
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