学术报告-Parallel-in-time preconditioners for the sinc-Nyström systems

题目：Parallel-in-time preconditioners for the sinc-Nyström systems

主讲人：刘俊

时 间：2023年10月26月（周四）上午11：00-12：00

地 点：东校区二教504腾讯会议978-2914-3642

主讲人简介：

刘俊，副教授，现任职于美国南伊利诺伊大学爱德华兹维尔分校(SIUE)数学和统计系。2010年硕士毕业于华南师范大学，2015年博士毕业于南伊利诺伊大学卡本代尔分校(SIUC)；主要研究方向：数值偏微分方程及其最优控制问题，数值线性代数和工程计算中的各类快速算法；到目前为止共发表各类期刊文章五十多篇，论文发表的杂志包括SIMAX, SISC, Inverse Problems, Adv. Comput Math, Numer. Algorithms, Mathematical Biosciences等国际知名杂志。

内容提要：

Abstract:

The sinc-Nyström method is a high-order numerical method in time for evolutionary differential equations. But it has to solve all the time steps in one shot (i.e., all-at-once), which results in a large-scale structured nonsymmetric dense linear system. In this talk, we introduce parallel-in-time preconditioners for such dense linear systems. The proposed preconditioner is a low-rank perturbation of the original matrix, and it has two advantages. First, the eigenvalues of the preconditioned system are highly clustered with some uniform bounds which are independent of the mesh parameters. Second, the preconditioner can be computed in parallel-in-time via diagonalization technique. The effectiveness of our proposed preconditioners is illustrated by several numerical examples.

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2023年10月24日