学术报告：12月13号10:00-11:00，美国伍斯特理工学院--郝朝鹏

报告人

郝朝鹏

单位

美国伍斯特理工学院

报告题目

High-order   numerical methods for integral fractional Laplacian: analysis, algorithm and   applications

报告时间

12月13日周五

10：00-11：00

地点

太阳成集团tyc234cc官网   第二报告厅

邀请人

孙志忠 曹婉容杜睿

报告摘要

The fractional Laplacian is a promising mathematical   tool due to its ability to capture the anomalous diffusion and model the   complex physical phenomenon with long range interaction. One of important   applications of fractional Laplacian is a turbulence intermittency model of   fractional Navier-Stokes equation. However efficient computation of this   model on bounded domains is challenging as highly accurate and efficient   numerical methods are not yet available. The bottleneck for efficient   computation lies in the low accuracy and high computational cost of discretizing   the fractional Laplacian operator.

The main reasons are due to nonlocal nature   and intrinsic singularity of the fractional Laplacian. To reduce the   complexity and computational cost, we consider two numerical methods, finite   difference and spectral method with quasi-linear complexity, which are   summarized as follows.

（1）We propose a simple and   easy-to-implement fractional centered difference approximation to the   fractional Laplacian on a uniform mesh using generating functions.The weights or coefficients of the   fractional centered formula can be readily computed using the fast Fourier   transform.

（2）We present spectral Galerkin methods   to accurately solve the fractional advection-diffusion-reaction equations. In   spectral methods on a ball, the evaluation of fractional Laplacian operator   can be straightforward thanks to the pseudo-eigen relation. For general   smooth computational domains, we propose the use of spectral methods enriched   by singular functions which characterizes the inherent boundary singularity   of the fractional Laplacian.

报告人简介

郝朝鹏博士于2010年-2017年在太阳成集团tyc234cc官网攻读研究生，并获得博士学位。2015-2017年攻读博士学位期间，先后在美国普渡大学和美国伍斯特理工学院进行为期两年的博士联合培养。2017年开始在美国伍斯特理工学院担任助理研究员并攻读博士学位。已在SIAM Journal   on Numerical Analysis, SIAM Journal on Scientific Computing, Journal of   Computational Physics 等期刊发表文章十余篇。 目前研究兴趣包括随机微分方程数值解、分数阶微分方程数值解、机器学习和深度神经网络等。