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鲁汪涛研究员学术报告

  发布日期:2017-8-11  浏览量:262


报告题目: Babich-like ansatz for 3D point-source Maxwell's equation in an inhomogeneous medium at high frequencies

报 告 人:鲁汪涛研究员 (浙江大学)

报告时间: 2017815(周二)  10:30-11:30

报告地点: 磬苑校区数学科学学院H306

报告摘要We propose a novel Babich-like ansatz consisting of an infinite series of dyadic coefficients (three-by-three matrices) and spherical Hankel functions for solving point-source Maxwell's equations in an inhomogeneous medium so as to produce the so-called dyadic Green's function. Using properties of spherical Hankel functions, we derive governing equations for the unknown asymptotics of the ansatz including the traveltime function and dyadic coefficients. By proposing matching conditions at the point source, we rigorously derive asymptotic behaviors of these geometrical-optics ingredients near the source so that their initial data at the source point are well-defined. To verify the feasibility of the proposed ansatz, we truncate the ansatz to keep only the first two terms, and we further develop partial differential equation--based Eulerian approaches to compute the resulting asymptotic solutions. Since the system of governing equations for each dyadic coefficient is strongly coupled, we introduce auxiliary variables to transform these strongly coupled systems into decoupled scalar equations. Furthermore, we develop high-order Lax--Friedrichs weighted essentially nonoscillatory schemes for computing these auxiliary variables so that the Green's function can be constructed. Numerical examples demonstrate that our new ansatz yields a uniform asymptotic solution in the region of space containing a point source but no other caustics. 

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                                              数学科学学院

                                            2017810

 

专家简介: 鲁汪涛,2012年博士毕业于香港城市大学和中国科学技术大学。毕业后先在香港城市大学从事博士后研究,并于2013年到2017年在密歇根州立大学任职副研究员。2016年入选第十三批国家“千人计划”青年项目。2017年8月到浙江大学工作。主要从事计算电磁学、高频波和几何光学法研究。在 Journal of Computational Physics,SIAM Multiscale Modeling and Simulation,Geophysics等国际权威期刊上发表SCI收录论文20多篇。

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