学术报告

24-04-2022

学术报告——Asymptotic analysis for time-dependent PDE models with small holes and applications


报告人:王海兵教授(东南大学)

时间:4月26日 14:30-15:30

地点: 线下:环境楼316报告厅

           线上:腾讯会议 516-280-570 密码 1046

报告内容:In this talk, we consider two time-dependent PDE models with a cluster of small holes. Based on the time-domain boundary integral equation method, we derive the asymptotic expansion of the solution as the size of the holes goes to zero. Under certain geometrical constraints on the size and the minimum distance of the holes, we show that the solution is approximated by a linear combination of point-sources where the weights are given by the capacitance of each hole. A rigorous justification of the asymptotic expansion is shown under natural conditions on the cluster of holes. As an application of the asymptotic expansion, we derive, in the limit case when the holes are densely distributed and occupy a bounded domain, the equivalent effective medium that generates, approximately, the same solution as the cluster of holes. Finally, we numerically verify the asymptotic expansions by comparing the asymptotic approximations with the numerical solutions via the finite element method.

告人简介:王海兵,东南大学亚博玩球平台教授,博士研究生导师,主要从事数学物理反问题的研究。2012年获得北海道大学和东南大学的理学博士学位。现任中国数学会计算数学分会常务理事。目前正主持一项国家自然科学基金面上项目,已发表论文三十余篇,代表性研究成果发表于SIAM系列,IP, JDE, JCP等学术刊物。

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