Efficient preconditioning for an optimal control problem with the time-periodic stokes equations

被引：0

作者：

Krendl, Wolfgang ^{[1
]}

Simoncini, Valeria ^{[2
]}

Zulehner, Walter ^{[3
]}

机构：

[1] Doctoral Program Mathematics, Johannes Kepler University Linz, Altenberger Straße 69, Linz

[2] Dipartimento di Matematica, Università di Bologna, Piazza di Porta S, Donato 5, Bologna

[3] Institute of Computational Mathematics, Johannes Kepler University Linz, Altenberger Straße 69, Linz

来源：

Lecture Notes in Computational Science and Engineering | 2015年 / 103卷

关键词：

Numerical methods - Navier Stokes equations - Optimal control systems - Matrix algebra;

D O I：

10.1007/978-3-319-10705-9__47

中图分类号：

学科分类号：

摘要：

For the optimal control problem with time-periodic Stokes equations a practical robust preconditioner is presented. The discretization of the corresponding optimality system leads to a linear system with a large, sparse and complex 4-by-4 block matrix in saddle point form. We present a decoupling strategy, which reduces the system to two linear systems with a real 4-by-4 block matrix. Based on analytic results on preconditioners for time-harmonic control problems in Krendl et al. (Numer Math 124(1):183-213, 2013), a practical preconditioner is constructed, which is robust with respect to the mesh size h, the frequency ! and the control parameter_. The result is illustrated by numerical examples with the preconditioned minimal residual method. Finally we discuss alternative stopping criteria. © Springer International Publishing Switzerland 2015.

引用

页码：479 / 487

页数：8