Model order reduction for parametrized nonlinear hyperbolic problems as an application to uncertainty quantification

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:348

Article

Crisovan, R.¹  Torlo, D.¹  Abgrall, R.¹  Tokareva, S.¹ 

[1] Inst Math, Winterthurstr 190, CH-8057 Zurich, Switzerland

关键词: Reduced order modeling;    Nonlinear hyperbolic problems;    UQ;    Empirical interpolation method;    POD Greedy;    Residual distribution;   

DOI  :  10.1016/j.cam.2018.09.018

来源: Elsevier

【 摘 要 】

In this work, we present a model order reduction (MOR) technique for hyperbolic conservation laws with applications in uncertainty quantification (UQ). The problem consists of a parametrized time dependent hyperbolic system of equations, where the parameters affect the initial conditions and the fluxes in a non- linear way. The procedure utilized to reduce the order is a combination of a Greedy algorithm in the parameter space, a proper orthogonal decomposition (POD) in time and empirical interpolation method (EIM) to deal with non-linearities (Drohmann, 2012). We provide under some hypothesis an error bound for the reduced solution with respect to the high order one. The algorithm shows small errors and savings of the computational time up to 90% in the UQ simulations, which are performed to validate the algorithm. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free