@Article{CiCP-34-787,
author = {Yang , ZihaoWang , XintongGuan , XiaofeiHuang , Jizu and Wu , Xixin},
title = {A Normalizing Field Flow Induced Two-Stage Stochastic Homogenization Method for Random Composite Materials},
journal = {Communications in Computational Physics},
year = {2023},
volume = {34},
number = {3},
pages = {787--812},
abstract = {<p style="text-align: justify;">The traditional stochastic homogenization method can obtain homogenized
solutions of elliptic problems with stationary random coefficients. However, many
random composite materials in scientific and engineering computing do not satisfy the
stationary assumption. To 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 coefficients. By 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 problems. Without the stationary
assumption, the number of cell problems is large and the corresponding computational
cost is high. To 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
method. Numerical 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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0007},
url = {http://global-sci.org/intro/article_detail/cicp/22024.html}
}