报告摘要：Time-dependent fractional partial differential equations typically require huge amounts of memory and computational time, especially for long-time integration, which taxes computational resources heavily for high-dimensional problems. Here, we first analyze existing numerical methods of sum-of-exponentials for approximating the kernel function in constant-order fractional operators, and identify the current pitfalls of such methods. In order to overcome the pitfalls, an improved sum-of-exponentials is developed and verified. We also present several sum-of-exponentials for the approximation of the kernel function in variable-order fractional operators. Subsequently, based on the sum-of-exponentials, we propose a unified framework for fast time-stepping methods for fractional integral and derivative operators of constant and variable orders. We test the fast method based on several benchmark problems, including fractional initial value problems, the time-fractional Allen–Cahn equation in two and three spatial dimensions, and the Schrodinger equation with nonreflecting boundary conditions, demonstrating the efficiency and robustness of the proposed method. The convergence analysis of the fast method is also displayed. The results show that the present fast method significantly reduces the storage and computational cost especially for longtime integration problems.

报告人简介：曾凡海，山东大学数学学院教授、博士生导师。2005年在西北工业大学数学系获学士学位，2014年在上海大学数学系获得博士学位。2014年至2020年分别在美国布朗大学、澳大利亚昆士兰科技大学和新加坡国立大学做博士后研究。2020年获得“山东大学杰出中青年学者”称号。2015年合作出版专著1部、在SINUM, SISC, JSC, JCP和CMAME等国际期刊上发表论文30余篇，SCIE他引1000余次。

报告时间：2024年5月27日15:30

报告地点：北衡楼1421