报告题目：The bilateral preconditioning for an L2-type all-at-once system arising from time-space fractional Bloch-Torrey equations

报告时间：2022年04月27日，星期三，16:00-17:00

腾讯会议：946 329 449

报告专家：顾先明副教授，西南财经大学经济数学学院

报告摘要：

Time-space fractional Bloch-Torrey equations (TSFBTEs) are developed by some researchers to investigate the relationship between diffusion and fractional-order dynamics. In this paper, we first propose a second-order implicit difference scheme for TSFBTEs by employing the recently proposed L2-type formula [A. A. Alikhanov, C. Huang, Appl. Math. Comput. (2021): 126545]. Then, we prove the stability and the convergence of the proposed scheme. Based on this numerical scheme, an L2-type all-at-once system is derived. In order to solve this system in a parallel-in-time pattern, a bilateral preconditioning technique is designed to accelerate the convergence of Krylov subspace solvers according to the special structure of the coefficient matrix of the system. We theoretically show that the condition number of the preconditioned matrix is uniformly bounded by a constant for the time fractional order α∈(0, 0.3624). Numerical results are reported to show the efficiency of our method.

报告专家简介：

    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, IEEE-TKDE, CPC, JCP, JSC, BIT等国际知名SCI期刊上发表学术论文70篇，现担任国际SCI学术期刊《ScienceAsia》，《Journal of Function Space》，《Maejo International Journal of Science and Technology》，《Journal of Mathematics》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。