TY - JOUR
T1 - Multi-Modes Multiscale Approach of Heat Transfer Problems in Heterogeneous Solids with Uncertain Thermal Conductivity
AU - Zhang , Shan
AU - Yang , Zihao
AU - Guan , Xiaofei
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 69
EP - 93
PY - 2022
DA - 2022/10
SN - 15
DO - http://doi.org/10.4208/aamm.OA-2022-0048
UR - https://global-sci.org/intro/article_detail/aamm/21126.html
KW - Stochastic multiscale heat transfer problems, uncertainty quantification, MCEM-GMsFEM, multimodes expansion.
AB - <p style="text-align: justify;">Stochastic temperature distribution should be carefully inspected in the
thermal-failure design of heterogeneous solids with unexpected random energy excitations. Stochastic multiscale modeling for these problems involve multiscale and high-dimensional uncertain thermal parameters, which remains limitation of prohibitive
computation. In this paper, we propose a multi-modes based constrained energy minimization generalized multiscale finite element method (MCEM-GMsFEM), which can
transform the original stochastic multiscale model into a series of recursive multiscale models sharing the same deterministic material parameters by multiscale analysis. Thus, MCEM-GMsFEM reveals an inherent low-dimensional representation in
random space, and is designed to effectively reduce the complexity of repeated computation of discretized multiscale systems. In addition, the convergence analysis is
established, and the optimal error estimates are derived. Finally, several typical random fluctuations on multiscale thermal conductivity are considered to validate the
theoretical results in the numerical examples. The numerical results indicate that the
multi-modes multiscale approach is a robust integrated method with the excellent performance.</p>