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Preconditioners for Time-Harmonic Optimal Control Eddy-Current Problems

  • Owe Axelsson
  • Dalibor Lukáš
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10665)

Abstract

Time-harmonic formulations enable solution of time-dependent PDEs without use of normally slow time-stepping methods. Two efficient preconditioners for the discretized parabolic and eddy current electromagnetic optimal control problems, one on block diagonal form and one utilizing the two by two block structure of the resulting matrix, are presented with simplified analysis and numerical illustrations. Both methods result in tight eigenvalue bounds for the preconditioned matrix and very few iterations that hold uniformly with respect to the mesh, problem and method parameters, with the exception of the dependence on reluctivity for the block diagonal preconditioner.

Keywords

Preconditioning Krylov subspace methods Optimal control Eddy currents Time-harmonic 

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Institute of GeonicsCzech Academy of SciencesOstrava-PorubaCzech Republic
  2. 2.VŠB-Technical University of OstravaOstrava-PorubaCzech Republic

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