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Multiscale model reduction for stochastic elasticity problems using ensemble variable-separated method

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2023年 421卷

作者： Guan, Xiaofei Jiang, Lijian Wang, Yajun Tongji Univ Sch Math Sci Shanghai Peoples R China

Elasticity is a fundamental model in mechanics and material sciences. In the article, we present an ensemble variable-separated multiscale method for elasticity problems in random media. A variable-separated method is utilized to provide a low-rank approximation for random fields. The variable-separated method is integrated with the Generalized Multiscale Finite Element method (GMsFEM) to obtain an efficient reduced model. To this end, a few local problems are solved for snapshots to construct the multiscale basis functions in GMsFEM. An ensemble method is used to construct stochastic basis functions shared by a series of elasticity equations, and a residual decomposition is adopted to calculate the deterministic physical components for all ensemble members. The ensemble variable-separation is used to solve the local problems of the multiscale basis functions and achieves efficient online-computation for the basis. Then, under the Galerkin projection of the generalized finite element method, the solutions of stochastic elasticity problems are projected onto the low-dimensional space spanned by the online multiscale basis functions. This renders an effective coarse model. The ensemble variable-separated multiscale method is applied to steady-state elastic deformation and elastic wave propagation in random media. A few numerical results are carried out to demonstrate the accuracy and efficiency of the presented method. (c) 2022 Elsevier B.V. All rights reserved.

关键词： Multiscale basis functions Elasticity problems Random media ensemble variable-separated method

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