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      Diagonalization-based Preconditioner for optimal control of wave

      發布者:文明辦發布時間:2020-11-20瀏覽次數:10


      主講人:吳樹林  東北師范大學教授


      時間:2020年11月21日16:00


      地點:騰訊會議 251 894 862


      舉辦單位:數理學院


      主講人介紹:2010年5月畢業于華中科技大學,獲計算數學專業博士學位,研究方向為發展方程快速算法設計、分析與應用。有國內、國外和香港地區博士后研究經歷,現任職于東北師范大學數學與統計學院。獲國家自然科學基金面上項目資助、中國博士后科學基金特別資助及四川省杰出青年基金資助,  2017年入選中國科協“青年人才托舉工程”。時間并行算法ParaDiag  主要創始人,該算法具有網格尺寸無關的快速、穩健收斂速度,解決了以Parareal為代表的主流時間并行算法求解波傳導問題時面臨的本質困難。2020年5月,ParaDiag算法獲得國際時間并行計算科學委員會的批準,在該領域官方網站上進行宣傳和推廣(官網主頁:  http://parallel-in-time.org/codes/paradiag.html)。近年來,在時間并行計算研究領域以第一作者或通訊作者身份署名的研究成果多次發表在計算數學領域的期刊上,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。


      內容介紹: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.

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