Advances in Computational Mathematics

, Volume 41, Issue 2, pp 457–488 | Cite as

Second-order approximation and fast multigrid solution of parabolic bilinear optimization problems

Article

Abstract

An accurate and fast solution scheme for parabolic bilinear optimization problems is presented. Parabolic models where the control plays the role of a reaction coefficient and the objective is to track a desired trajectory are formulated and investigated. Existence and uniqueness of optimal solution are proved. A space-time discretization is proposed and second-order accuracy for the optimal solution is discussed. The resulting optimality system is solved with a nonlinear multigrid strategy that uses a local semismooth Newton step as smoothing scheme. Results of numerical experiments validate the theoretical accuracy estimates and demonstrate the ability of the multigrid scheme to solve the given optimization problems with mesh-independent efficiency.

Keywords

Multigrid methods Newton methods Finite differences Parabolic partial differential equations Bilinear control ptimal control theory 

AMS:

49K20 49J20 65M55 65C20 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institut für MathematikUniversität WürzburgWürzburgGermany
  2. 2.Research Center on Mathematical Modelling MODEMATEscuela Politécnica NacionalQuitoEcuador

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