A preconditioner for optimal control problems, constrained by Stokes equation with a time-harmonic control

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• 作者：Owe Axelsson^a ; ^b ; ^{owe.axelsson@it.uu.se" class="auth_mail" title="E-mail the corresponding author} ; Shiraz Farouq^b ; ^{shiraz.farouq@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Maya Neytcheva^b ; ^{maya.neytcheva@it.uu.se" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Optimal control ; Time-harmonic Stokes problem ; Preconditioning
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：310
• 期：Complete
• 页码：5-18
• 全文大小：504 K

文摘

In this article we construct an efficient preconditioner for solving the algebraic systems arising from discretized optimal control problems with time-periodic Stokes equations, based on a preconditioning technique for stationary Stokes-constrained optimal control problems, considered in an earlier paper by the authors. A simplified analysis of the derivation of the preconditioner and its properties is presented. The preconditioner is fully parameter-independent and the condition number of the corresponding preconditioned matrix is bounded by 2. The so-constructed preconditioner is favourably compared with another robust preconditioner for the same problem.