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

内容簡介：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.

報告人：華中科技大學   王海永   副教授

報告人簡介：2001年9月考入中南大學數學統計學院；2005年7月畢業、獲理學學士學位；2005年9月攻讀中南大學計算數學專業碩士；2007年9月攻讀中南大學計算數學專業博士。2011年3月-2012年12月在比利時魯汶大學計算科學系做博士後。2013年在華中科技大學工作，任副教授，并工作至今。主要從事高振蕩問題數值方法、數值積分、譜方法和重心插值等領域的研究。主持國家自然科學基金面上項目1項，國家自然科學基金青年項目1項。在計算數學國際權威期刊已發表學術論文10多篇，其中部分結果被英國皇家院士Trefethen收錄其書《Approximation Theory and Approximation Practice》中。

時  間：2018年1月5日（周五）下午4：00始

地  點：南海樓330室

熱烈歡迎廣大師生參加!

太阳集团1088vip/網絡空間安全學院

2018年1月3日