讲座论坛
荔园数学讲坛: A preconditioning technique for an all-at-once system from Volterra subdiffusion equations with graded time steps
发布时间:2022-06-14 10:25:00 771

内容摘要: 

Volterra subdiffusion problems with weakly singular kernel describe the dynamics of subdiffusion processes well. The graded L1 scheme is often chosen to discretize such problems since it can handle the singularity of the solution near t = 0. In this paper, we propose a modification. We first split the time interval [0, T] into [0, T_0] and [T_0, T], where T_0 (0 < T_0 < T) is reasonably small. Then, the graded L1 scheme is applied in [0, T_0], while the uniform one is used in [T_0, T]. Our all-at-once system is derived based on this strategy. In order to solve the arising system efficiently, we split it into two subproblems and design two preconditioners. Some properties of these two preconditioners are also investigated. Moreover, we extend our method to solve semilinear subdiffusion problems. Numerical results are reported to show the efficiency of our method.

主讲人简介: 

顾先明,西南财经大学经济数学学院副教授,硕士生导师。2017年6月在电子科技大学获得博士学位,2014-2016年获荷兰格罗宁根大学Ubbo Emmius奖学金资助赴该校攻读第二博士学位,2019年7月-11月在澳门大学数学系从事博士后研究。曾连续三年获得博士国家奖学金,也获得了电子科大学生最高荣誉“成电杰出学生”。主要研究方向为数值线性代数和分数阶偏微分方程快速(并行)数值解法等。截止目前,已在包括IEEE-TMTT, IEEE-TAP, CPC, JCP, JSC等国际知名SCI期刊上发表学术论文73篇,现担任国际SCI学术期刊《ScienceAsia》,《J. Funct. Space》,《Maejo Int. J. Sci. Technol.》,《J. Math.》和《Demonstr. Math.》学术编委。参与编写和出版学术专著《Krylov子空间算法与预处理技术及其应用》一部,2021年获得四川省数学会首届应用数学奖(三等奖),现主持国家自然科学基金青年项目和四川省应用基础研究项目各1项。