题目：A rational approximation scheme for computing Mittag-Leffler function with discrete elliptic operator as input

时间：2022年4月2日（星期六）20:00-22:00

腾讯会议：202-332-824会议密码：220402

摘要: In this work, we propose a new scheme based on numerical quadrature to calculate the two-parameter Mittag-Leffler function with discrete elliptic operator as input. Except pure mathematical interest from approximation theory, our consideration also arises from solving sub-diffusion equations numerically with time-independent diffusion coefficient. We obtain the scheme by applying Gauss-Legendre quadrature rule for the integral representation of the Mittag-Leffler function. Rigorous error analysis is carried out which shows that the scheme converges exponentially with the increase of quadrature nodes. The computational cost of the algorithm is solving K sparse linear systems with K the number of quadrature nodes. It is worth to point out that the scheme is completely parallel which can save much time if the dimension of the discrete elliptic operator is very large. Some numerical tests are provided to verify the efficiency and robustness of our scheme.

报告人简介：段北平，深圳北理莫斯科大学数学系助理研究员。2016年9月至2018年6月在Texas A&M University数学系访问。22019年6月博士毕业于中南大学数学与统计学院，随后在中国工程物理研究院北京计算科学研究中心从事博士后研究。研究方向为计算几何流、Navier-Stokes两相流等界面问题以及非光滑函数逼近问题，主要成果发表于IMA J. Numerical Analysis, J. Scientific Computing，J. Computational Physics等国际主流学术期刊。