报告人：王海兵 教授

会议时间：2022/09/14 10:00-11:30 

腾讯会议：897-904-341

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报告摘要：

Consider the time-domain acoustic scattering problem by a cluster of small sound-soft obstacles. Based on the retarded boundary integral equation method, we derive the asymptotic expansion of the scattered field 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 scattered field is approximated by a linear combination of point-sources where the weights are given by the capacitance of each hole and the causal signals (of these point-sources) can be computed by solving a, retarded in time, linear algebraic system. A rigorous justification of the asymptotic expansion and the unique solvability of the linear algebraic system are 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 acoustic medium (an equivalent mass density characterized by the capacitance of the holes) that generates, approximately, the same scattered field as the cluster of holes. Finally, we numerically verify the asymptotic expansions by comparing the asymptotic approximations with the numerical solutions of the scattered fields via the finite element method.

报告人简介：

王海兵，东南大学数学学院教授，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。

邀请人：杜锐