报告题目 (Title)：Optimal Rotated Block-Diagonal Preconditioning for Discretized Optimal Control Problems Constrained with Fractional Time-Dependent Diffusive Equations（带分数时间扩散方程约束的离散最优控制问题的最优旋转块对角预条件处理)

报告人 (Speaker)： 白中治 教师（中国科学院数学与系统科学研究院）

报告时间 (Time)：2023年10月20日(周五) 14:00

报告地点 (Place)：校本部F309

邀请人(Inviter)：张建军

主办部门：理学院数学系

报告摘要：For a class of optimal control problems constrained with certain time- and space-fractional diffusive equations, by making use of mixed discretizations of temporal finite-difference and spatial finite-element schemes along with Lagrange multiplier approach, we obtain specially structured block two-by-two linear systems. We demonstrate positive definiteness of the coefficient matrices of these discrete linear systems, construct rotated block-diagonal preconditioning matrices, and analyze spectral properties of the corresponding preconditioned matrices. Both theoretical analysis and numerical experiments show that the preconditioned Krylov subspace iteration methods, when incorporated with these rotated block-diagonal preconditioners, can exhibit optimal convergence property in the sense that their convergence rates are independent of both discretization step sizes and problem parameters, and their computational workloads are linearly proportional with the number of discrete unknowns.