Multigrid Optimization Methods for the Optimal Control of Convection–Diffusion Problems with Bilinear Control

被引：0
作者：
A. Borzì
E.-J. Park
M. Vallejos Lass
机构：
[1] Universität Würzburg,Institut für Mathematik
[2] Emil-Fischer-Straße 30,Department of Computational Science and Engineering
[3] Yonsei University,Institute of Mathematics
[4] University of the Philippines,Department of Mathematics
[5] Technische Universität Darmstadt,undefined
来源：
Journal of Optimization Theory and Applications | 2016年 / 168卷
关键词：
Optimal control; Multigrid methods; Convection–diffusion; Bilinear control; Finite differences; 49J20; 49K20; 65N06; 65N55;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Optimal control problems, governed by convection–diffusion equations with bilinear control, are studied. For the realization of the numerical solution, the multigrid for optimization method together with finite difference discretization is utilized and investigated. In addition, the extension to constrained optimal control problems with bilinear control is considered. Results of numerical experiments show the computational performance of the proposed multigrid scheme in solving optimal control problems subject to a convection–diffusion equation with bilinear control. We obtain that the proposed multigrid strategy accelerates classical one-grid optimization schemes and inherits the order of convergence of the finite difference discretization. Moreover, the mesh independence principle is obtained, which is a typical characterization of a multigrid strategy.
引用
收藏
页码：510 / 533
页数：23
相关论文
共 50 条
  • [1] Baek H(2010)A multigrid method for an optimal control problem of a diffusion–convection equation J. Korean Math. Soc. 47 83-100
  • [2] Kim SD(2004)An efficient algebraic multigrid method for solving optimality systems Comput. Vis. Sci. 7 183-188
  • [3] Lee H(2009)A priori error estimates for elliptic optimal control problems with bilinear state equation J. Comput. Appl. Mech. 230 781-802
  • [4] Borzì A(2011)A robust multigrid method for elliptic optimal control problems SIAM J. Numer. Anal. 49 1482-1503
  • [5] Borzì G(2008)Multigrid optimization methods for linear and bilinear elliptic optimal control problems Computing 82 31-52
  • [6] Kröner A(2005)A multigrid scheme for elliptic constrained optimal control problems Comput. Optim. Appl. 31 309-333
  • [7] Vexler B(2002)Accuracy and convergence properties of the finite difference multigrid solution of an optimal control optimality system SIAM J. Control Optim. 41 1477-1497
  • [8] Schöberl J(1997)Adaptive refinement for convection–diffusion problems based on a defect-correction technique and finite difference method Computing 58 1-30
  • [9] Simon R(2007)Optimal control of the convection–diffusion equation using stabilized finite element methods Numer. Math. 106 349-367
  • [10] Zulehner W(2010)Local error estimates for SUPG solutions of advection-dominated elliptic linear-quadratic optimal control SIAM J. Numer. Anal. 47 4607-4638
12345