报告人：朱睦正

时间：12月11日（周六）下午4：00-5:00

地点：理工楼631

题目：On TDS-PCG Iteration Method with Circulant Preconditioners for Solving the Space Fractional Coupled Nonlinear Schrödinger Equations

报告摘要：The goal of this paper is to solve the complex symmetric linear systems generated from the discretization of the space fractional coupled nonlinear Schrödinger (CNLS) equations, whose coefficient matrix is equal to the sum of a symmetric positive definite Toeplitz matrix and a Hermitian positive definite complex diagonal matrix. In order to make the best use of the full Toeplitz structure of the coefficient matrix, a new Toeplitz and diagonal splitting (TDS) is given and the corresponding TDS iteration method is proposed to solve the discretized linear systems, then two circulant preconditioners based on Strang’s and T. Chan’s circulant approximation, are proposed to accelerate the convergence of the preconditioned conjugated gradient (PCG) method for solving the first linear sub-system in the TDS method. Theoretical analysis and numerical experiments demonstrate that the TDS method is unconditional convergence and the TDS-PCG inner-outer iteration method with two circulant preconditioners to solve the discretization linear systems of the space fractional CNLS equations is feasible and efficient.

报告人简介

朱睦正，博士，教授，河西学院304am永利集团官网副院长。研究方向为：数值线性代数。近年来主持完成国家基金1项，甘肃省教育厅科研项目1项，河西学院科研项目2项，校级重点课程建设项目1项，教学研究项目1项，发表高水平SCI论文20余篇。获得甘肃省高等学校科技进步三等奖1项。

报告人：曾闽丽

时间：12月11日（周六）下午5：00-6:00

地点：理工楼631

题目：The RSS-like iteration method for block two-by-two linear systems from time-periodic parabolic optimal control problems

报告摘要：We present a respectively scaled splitting-like (RSS-like) iteration method for block two-by-two linear systems from time-periodic parabolic optimal control problems. The detailed spectral properties of the RSS-like preconditioned matrix are analyzed and the unconditionally convergent properties of the RSS-like iteration method are described. Furthermore, we propose the optimal parameters of the RSS-like preconditioner. Numerical experiments are used to compare with some classical and recent efficient methods to show the efficiency of the new methods.

报告人简介

曾闽丽，博士，莆田学院数学与金融学院教授，华侨大学兼职硕士生导师。2017年入选福建省杰出青年培育计划人选、获莆田市“壶兰英才”青年拔尖人才称号。2018年获莆田市“巾帼标兵”、“美丽青年先锋章”、“三八红旗手”等荣誉称号。主要研究方向为数值线性代数、PDE优化问题离散系统及分数阶偏微分方程结构化离散系统的快速算法等。先后赴美国新奥尔良大学、英国伯明翰大学、澳门大学、中国科学院数学与系统科学研究院、南京大学合作访问研究。先后主持国家基金3项，福建省科技厅项目1项，福建省教育厅中青年科研项目及校内项目若干项。以第一作者在包括 Applied Mathematics and Computation、Computers and Mathematics with Applications、Journal of Computational and Applied Mathematics 等国际知名SCI期刊上发表论文近30篇。

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2021年12月10日