报告题目：Rational spectral-Galerkin method for nonlocally strongly damped nonlinear wave system involving fractional Laplacian in unbounded domains

主讲人：郭士民 教授 （西安交通大学）

时 间：2022年10月14日（周五）16:00 —17:00

地  点：腾讯会议（会议号：840-237-464）

主办单位：理学院

摘要：

In this talk, we develop a dissipation-preserving, linearized, and time-stepping-varying spectral method for nonlocally strongly damped nonlinear wave system in multidimensional unbounded domains R^d (d=1, 2, and 3), where the nonlocal nature is described by the fractional Laplacian. We employ the rational spectral-Galerkin method using rational basis (or mapped Gegenbauer functions) for the spatial approximation. Inspired by the exponential scalar auxiliary variable (ESAV) approach, we apply the Crank-Nicolson scheme for the temporal discretization to capture the intrinsic dissipative properties of the model equations. When used in conjunction with the adaptive time-stepping strategy, the proposed scheme possesses the high efficiency without sacrificing accuracy. The existence, uniqueness, and nonlocal energy dissipation law of the fully discrete scheme are established.

主讲人简介:

郭士民，2013年获得计算数学专业博士学位，同年留校任教，现为西安交通大学数学与统计学院教授、博士生导师，主要研究方向为非局部/分数阶微分方程的高精度数值算法、谱方法与计算等离子体物理学；以第一作者在SIAM Journal on Scientific Computing、Journal of Computational Physics等国际期刊上发表SCI论文30余篇，单篇他引最高次数为280余次(Google学术)，另有2篇论文入选“ESI高被引论文”；主持国家自然科学基金面上项目等多项国家级、省部级科研项目，荣获2019年度陕西省自然科学奖二等奖 (第二完成人)  。