报告人：关晓飞 同济大学数学系 副教授
报告题目：Multi-modes multiscale approach of heat transfer problems in heterogeneous solids with uncertain thermal conductivity
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 uncertain thermal conductivity, high-dimensional and multiscale features, which remains limitation of prohibitive computation. In this paper, we propose an 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 stochastic disturbance on the mean value of uncertain thermal conductivity are considered to validate the theoretical results in the numerical examples. The numerical results indicate that the multi-modes multiscale model is a robust integrated method with the excellent performance.