Efficient model reduction of parametrized systems by matrix discrete empirical interpolation

JOURNAL OF COMPUTATIONAL PHYSICS

卷:303

Article

Negri, Federico¹  Manzoni, Andrea¹  Amsallem, David² 

[1] Ecole Polytech Fed Lausanne, CMCS MATHICSE SB, Stn 8, CH-1015 Lausanne, Switzerland

[2] Stanford Univ, Dept Aeronaut & Astronaut, Stanford, CA 94305 USA

关键词: Model order reduction;    Discrete empirical interpolation;    System approximation;    Proper orthogonal decomposition;    Reduced basis methods;   

DOI  :  10.1016/j.jcp.2015.09.046

来源: Elsevier

【 摘 要 】

In this work, we apply a Matrix version of the so-called Discrete Empirical Interpolation (MDEIM) for the efficient reduction of nonaffine parametrized systems arising from the discretization of linear partial differential equations. Dealing with affinely parametrized operators is crucial in order to enhance the online solution of reduced-order models (ROMs). However, in many cases such an affine decomposition is not readily available, and must be recovered through (often) intrusive procedures, such as the empirical interpolation method (EIM) and its discrete variant DEIM. In this paper we show that MDEIM represents a very efficient approach to deal with complex physical and geometrical parametrizations in a non-intrusive, efficient and purely algebraic way. We propose different strategies to combine MDEIM with a state approximation resulting either from a reduced basis greedy approach or Proper Orthogonal Decomposition. A posteriori error estimates accounting for the MDEIM error are also developed in the case of parametrized elliptic and parabolic equations. Finally, the capability of MDEIM to generate accurate and efficient ROMs is demonstrated on the solution of two computationally-intensive classes of problems occurring in engineering contexts, namely PDE-constrained shape optimization and parametrized coupled problems. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free