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

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.