A multigrid scheme for solving convection–diffusion-integral optimal control problems

  • Duncan Kioi Gathungu
  • Alfio BorzìEmail author
Special Issue IMG 2016


The fast multigrid solution of an optimal control problem governed by a convection–diffusion partial-integro differential equation is investigated. This optimization problem considers a cost functional of tracking type and a constrained distributed control. The optimal control sought is characterized by the solution to the corresponding optimality system, which is approximated by a finite volume and quadrature discretization schemes and solved by multigrid techniques. The proposed multigrid approach combines a multigrid method for the governing model with a fast multigrid integration method. The convergence of this solution procedure is analyzed by local Fourier analysis and validated by results of numerical experiments.


Partial-integro differential equations Optimal control Multigrid scheme Finite differences 

Mathematics Subject Classification

47G20 49J20 49K20 65N55 65N06 



We would like to thank Volker Schulz for many helpful comments. This work was supported in part by the DAAD, by the European Union under Grant Agreement Nr. 304617 ‘Multi-ITN STRIKE - Novel Methods in Computational Finance’, and by the Würzburg-Wroclaw Center for Stochastic Computing.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Institut für MathematikUniversität WürzburgWürzburgGermany

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