报告人：孙海卫 教授
报告题目：All-at-once implementation of a time nonuniform mess scheme for sub-diffusion equation with initial time singularity
报告时间：2026年5月19日（周二）下午4:00—5:00
报告地点：云龙校区6号楼304报告厅
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
澳门大学数学系教授、博士生导师，1996年毕业于香港中文大学数学系获得博士学位。主要研究领域包括数值线性代数、偏微分方程数值解和计算金融学等。在SIAM系列期刊SISC，SINUM，SIMAX，以及Numer Math、JCP、JSC等计算数学杂志发表超过120篇高水平研究论文，担任过国际学术期刊EAJAM和IJCM编委，于2018年获得澳门特区政府颁发的自然科学二等奖，共主持澳门科技发展基金6项。
报告摘要：
In this talk, the geometrically increased time step size (GITSS) is proposed to discretize the Caputo fractional derivative. The resulting coefficient matrix can be written as a product of a diagonal multiplying a lower triangular Toeplitz matrix. Coordinately, the resulting coefficient matrix of the discretized sub-diffusion equations is a block diagonal plus a block tridiagonal Toeplitz matrix, that can be implemented all-at-once using the divide-and-conquer strategy with the block forward substitution method efficiently. Theoretically, the convergence of the GITSS method with L1 scheme is proved, which is like that by the classical graded mesh scheme. Numerical results show the efficiency and availability of the all-at-once treatment by the proposed method. Moreover, the Toeplitz-like structure brought by the GITSS will have more potential to develop the fast algorithm in the future.