Diagonalization-based Preconditioner for optimal control of wave


主讲人:吴树林  东北师范大学教授


地点:腾讯会议 251 894 862


主讲人介绍:2010年5月毕业于华中科技大学,获计算数学专业博士学位,研究方向为发展方程快速算法设计,分析与应用。有国内,国外和香港地区博士后研究经历,现任职于东北师范大学数学与统计学院。获国家自然科学基金面上项目资助,中国博士后科学基金特别资助及四川省杰出青年基金资助,  2017年入选中国科协“青年人才托举工程”。时间并行算法ParaDiag  主要创始人,该算法具有网格尺寸无关的快速,稳健收敛速度,解决了以Parareal为代表的主流时间并行算法求解波传导问题时面临的本质困难。2020年5月,ParaDiag算法获得国际时间并行计算科学委员会的批准,在该领域官方网站上进行宣传和推广(官网主页:  http://parallel-in-time.org/codes/paradiag.html)。近年来,在时间并行计算研究领域以第一作者或通讯作者身份署名的研究成果多次发表在计算数学领域的期刊上,例如SIAM系列(10),  Numer Math (1),ESAIM系列(2), J Comput Phys (4),J Sci Comput (2)以及IMA J Numer  Anal(2),等等。

内容介绍:Numerical computation of optimal control of wave equations is a challenging  problem, due to the lack of dissipativity of the constraint di erential  equation. Ecient preconditioner plays a central role for solving the  large-scale saddle point system and in this talk we will discuss a new one based  on directly diagonalizing the time discretization matrices. This results in  block spectral decomposition of the saddle point matrix and therefore  parallel-in-time computation is naturally permitted. Such a decomposition is  optimal in the sense that the condition number of eigenvector matrix equals to  1. The eigenvalues of the preconditioned matrix are tightly clustered around 1  and this con rms very well the fast and strongly robust convergence rate of  GMRES in practice. The idea can be generalized to eciently handle the optimal  control problems with a boxing type constraint of the control variable, via the  framework of two-point boundary value linear complementarity dynamics.