报告题目：On the time-domain acoustic waves reflected by a cluster of small sound-soft obstacles
报告人：王海兵教授，东南大学
报告时间：2020年11月1日下午14:00-16:00
报告地点：数理楼145小报告厅
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，男，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，2014年获得江苏省优秀博士学位论文，2016年入选江苏高校“青蓝工程”中青年学术带头人培养对象，2017年作为第二完成人获得教育部自然科学二等奖，2018年获得江苏省工业与应用数学学会第二届“工业与应用数学奖青年奖”。现任中国数学会计算数学分会常务委员。主持三项国家自然科学基金和一项江苏省自然科学基金，在SIAP, SIAM-MMS, IP, JCP等国内外刊物上发表三十余篇学术论文。