学术讲座《Fast algorithm for solving high frequency scattering problem in half space》

应我院许晓阳教授邀请，湖南师范大学汪波教授将于2026年11月5日来我校访问交流，并作学术报告，欢迎各位师生参加。

报告题目：Fast algorithm for solving high frequency scattering problem in half space

报告人：湖南师范大学 汪波教授

报告时间：2026年11月5日10：00 – 11：00

报告地点：临潼校区15教502-2会议室

报告内容简介：This talk presents a wideband fast multipole method (WBFMM) to accelerate the boundary integral solver of high-frequency Helmholtz scattering problems in a half-plane. By leveraging the half-plane Green’s function to formulate the boundary integral equation, the impedance boundary condition is satisfied inherently, eliminating the need for additional unknowns or equations on the half-plane boundary. The integral equation is discretized using a lowest-order collocation method. To accelerate the GMRES iterative solver for the resulting dense linear system, a novel WBFMM is developed. This method combines the classical WBFMM for the free-space component with a newly designed WBFMM for the reaction component. The latter is constructed within the same hybrid framework as its free-space counterpart but incorporates new far-field expansions, shift and translation operators, and an efficient discrete complex image method (DCIM) for evaluating high-order Sommerfeld integrals. Exponential convergence of these expansions and operators is established based on the well-known line-image representation of the reaction component. Numerical examples demonstrate the accuracy and efficiency of the proposed algorithm across a wide frequency range.

报告人简介：汪波，湖南师范大学数学与统计学院教授，国家高层次青年人才计划入选者。现任中国数学会计算数学分会理事、湖南计算数学应用软件学会副理事长、湖南省数学会常务理事。2011年获湖南师范大学博士学位，先后在新加坡国立大学、南洋理工大学及美国南卫理工会大学访学。主要从事超材料电磁场计算的间断有限元方法、波散射高精度数值方法、界面问题杂交间断伽辽金方法、多层媒质快速多极法及偏微分方程机器学习算法研究。主持国家自然科学基金5项等，发表论文30余篇。