Hao Dong, Professor, Xidian University

Liqun Cao, Professor

Higher-order multiscale method and its convergence analysis for nonlinear multiphysics coupling problems of composite structures

14:30-16:00 November 13(Thursday), S625

This study proposes a higher-order multiscale computational method tailored for two kinds of nonlinear multiphysics coupling problems of composite structures including nonlinear thermo-mechanical and nonlinear thermo-electric problems, which possess nonlinear temperature-dependent material properties and Joule heating effect. The innovative advancements of this work are the establishment of the high-accuracy multiscale models incorporating the higher-order correctors for periodic composite structures by employing the multiscale asymptotic approach and the Taylor series technique, along with a global error estimation that provides an explicit convergence rate for higher-order multiscale solutions. The proposed higher-order multiscale method can maintain the local balance of physical quantities enabling high-accuracy multiscale simulations. Furthermore, an efficient numerical algorithm featuring with off-line and on-line stages is presented meticulously. Extensive numerical experiments are conducted to showcase the competitive advantages of the proposed method for simulating the time-dependent nonlinear multiphysics coupling problems in composite structures, demonstrating not only exceptional numerical accuracy, but also reduced computational cost. In addition, some latest results about multiscale simulation of composite structures by deep neural networks will be discussed.

报告人简介：董灏，男，1991年生，现为西安电子科技大学教授，数学专业博士生导师、应用统计专业、力学专业硕士生导师，入选陕西高校优秀青年人才支持计划、陕西省科协/西安市科协青年人才托举计划。2013年7月本科毕业于西北工业大学应用数学系，2017年12月于西北工业大学获数学博士学位(导师：崔俊芝院士)，2018年5月-2021年6月西安电子科技大学博士后(导师：郑晓静院士)。主要从事复合材料结构的多尺度建模与计算、科学计算中的深度学习方法及其在材料计算中的应用等研究工作，已在SIAM系列、JCP、JSC、CMAME、CM、IJSAS、CS等计算数学、计算力学及计算材料学权威期刊上发表SCI论文40余篇，获批软件著作权3项。主持国自然(面上、青年)、国家博士后科学基金、省自然、省重点实验室开放课题各一项，获陕西省高校科学技术研究优秀成果特等奖、陕西省工业与应用数学学会青年科技奖等科研奖励六项。