题  目：A unified framework for asymptotic analysis and computation of Hankel transform

内容简介：Highly oscillatory integrals arise in many practical applications and their computation will be prohibitively expensive by using traditional quadrature rules. In the past decade several efficient methods were developed for integrals of Fourier-type such as asymptotic and Filon-type methods, Levin-type methods, numerical steepest descent methods and complex Gaussian methods. Among these methods, asymptotic methods play a fundamental role in clarifying the main contributions to the value of the integral from each type of critical point. In this talk, I will present a unified framework for asymptotic analysis and computation of Hankel transform with a general oscillator. I will show how to derive the asymptotic expansion of this transform, especially when the oscillator has zeros and stationary points. Moreover, two efficient numerical methods are derived to compute the Hankel transform numerically. Compared with traditional quadrature rules, both methods can be implemented with a fixed computational cost and their accuracy improves greatly with increasing frequency of oscillations.

报告人：华中科技大学   王海永   副教授

报告人简介：2001年9月考入中南大学数学统计学院；2005年7月毕业、获理学学士学位；2005年9月攻读中南大学计算数学专业硕士；2007年9月攻读中南大学计算数学专业博士。2011年3月-2012年12月在比利时鲁汶大学计算科学系做博士后。2013年在华中科技大学工作，任副教授，并工作至今。主要从事高振荡问题数值方法、数值积分、谱方法和重心插值等领域的研究。主持国家自然科学基金面上项目1项，国家自然科学基金青年项目1项。在计算数学国际权威期刊已发表学术论文10多篇，其中部分结果被英国皇家院士Trefethen收录其书《Approximation Theory and Approximation Practice》中。

时  间：2018年1月5日（周五）下午4：00始

地  点：南海楼330室

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信息科学技术学院/网络空间安全学院

2018年1月3日