题    目：Finite Difference Methods for fractional Laplacian of radial functions

主讲人：黄阳红

单    位：曼彻斯特大学

时    间：2025年1月4日 9:30

地    点：二楼会议室

摘    要：Numerical evaluation of nonlocal operators like the fractional Laplacian is more                          computationally intensive because of the dependence on the underlying function over the whole        space. On the other hand, many solutions to the fractional counterparts of classical semi-linear PDEs, especially ground states obtained via variational methods, are radial. In this talk, fractional Laplacian of radial functions in general dimensions will be considered with a kernel represented by a Gauss        hypergeometric function of the radial variables. The singular part of the kernel is isolated and then     treated with effective methods well studied in the one-dimensional context, while the regular part     can be evaluated with by classical quadrature. The method can be extended to general non-radial       functions that can be expanded using spherical harmonics, making it effective in the numerical study of fractional equations and complementing existing theoretical investigations.

简    介：黄阳红，本科毕业于香港浸会大学，博士毕业于美国加州大学洛杉矶分校，后在加拿大西蒙弗雷泽大学、英国帝国理工学院从事博士后研究工作，现任职于曼彻斯特大学数学系。研究兴趣包括非局部交互模型的精确及渐进稳态解，梯度流系统的粒子逼近，非局部方程的有限差分方法等，研究成果发表于SIAM系列，Bull. London Math. Soc., J. Funct. Anal.，Nonlinearity，J. Differential. Equations.,Physica D等期刊。