学术报告
题目：Optimal Rotated Block-Diagonal Preconditioningfor Discretized Optimal Control ProblemsConstrained with Fractional Time-Dependent Diffusive Equations
报告人：白中治 研究员单位：中国科学院数学与系统科学研究院
时 间：2022年3月12日（周六）上午 10：00-11：00
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报告人及报告内容简介：
白中治, 中国科学院数学与系统科学研究院研究员，曾任科学与工程计算国家重点实验室副主任。获得国家杰出青年科学基金，入选新世纪百千万人才工程计划（国家级人选），获得冯康科学计算奖、国家教育委员会科学技术进步奖、中国科学院青年科学家奖二等奖等。国务院政府特殊津贴获得者，国际线性代数学会会员，中国线性代数专业委员会委员。主要从事线性与非线性数值代数，并行算法及其应用，数值最优化方法与理论，微分代数方程组的数值方法，数值偏微分方程等方面的研究。
Abstract: 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 stepsizes and problem parameters, and their computational workloads are linearly proportional with the number of discrete unknowns.