Invited by School of Mathematics and Statistics, Ph.D. Muzheng Zhu from Hexi University and Mingli Zeng from Putian university will give lectures.

Reporter:Muzheng Zhu

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

Time：4:00 p.m.,Dec. 11th, 2021

Location: Room 631, Polytechnic building

Abstract：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.

Reporter：Mingli Zeng

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

Time：5:00 p.m.,Dec. 11th, 2021

Location: Room 631, Polytechnic building

Abstract: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.