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A Normalizing Field Flow Induced Two-Stage Stochastic Homogenization Method for random Composite Materials

Communications in Computational Physics 2023年第8期34卷 787-812页

作者： Zihao Yang Xintong Wang Xiaofei Guan Jizu Huang Xixin Wu School of Mathematics and Statistics Northwestern Polytechnical UniversityXi’an 710072China Institute of Mathematics Henan Academy of SciencesZhengzhou 450046China MOE Key Laboratory for Complexity Science in Aerospace Northwestern Polytechnical UniversityXi’an 710072China School of Mathematical Sciences Tongji UniversityShanghai 200092China LSEC Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

The traditional stochastic homogenization method can obtain homogenized solutions of elliptic problems with stationary random ***,many random composite materials in scientific and engineering computing do not satisfy the stationary *** overcome the difficulty,we propose a normalizing field flow induced two-stage stochastic homogenization method to efficiently solve the random elliptic problem with non-stationary *** applying the two-stage stochastic homogenization method,the original elliptic equation with random and fast oscillatory coefficients is approximated as an equivalent elliptic equation,where the equivalent coefficients are obtained by solving a set of cell *** the stationary assumption,the number of cell problems is large and the corresponding computational cost is *** improve the efficiency,we apply the normalizing field flow model to learn a reference Gaussian field for the random equivalent coefficients based on a small amount of data,which is obtained by solving the cell problems with the finite element *** results demonstrate that the newly proposed method is efficient and accurate in tackling high dimensional partial differential equations in composite materials with complex random microstructures.

关键词： Two-stage stochastic homogenization normalizing field flows multi-modes Monte Carlo method random composite materials non-stationary random

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