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PDE-constrained optimization of time-dependent 3D electromagnetic induction heating by alternating voltages

Please always quote using this URN:urn:nbn:de:0296-matheon-11146
  • This paper is concerned with a PDE-constrained optimization problem of induction heating, where the state equations consist of 3D time--dependent heat equations coupled with 3D time--harmonic eddy current equations. The control parameters are given by finite real numbers representing applied alternating voltages which enter the eddy current equations via impressed current. The optimization problem is to find optimal voltages so that, under certain constraints on the voltages and the temperature, a desired temperature can be optimally achieved. As there are finitely many control parameters but the state constraint has to be satisfied in an infinite number of points, the problem belongs to a class of semi--infinite programming problems. We present a rigorous analysis of the optimization problem and a numerical strategy based on our theoretical result.

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Metadaten
Author:Fredi Tröltzsch, Irwin Yousept
URN:urn:nbn:de:0296-matheon-11146
Referee:Fredi Tröltzsch
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2012/03/09
Release Date:2012/03/09
Institute:Technische Universität Berlin
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Kxx Optimality conditions / 49K20 Problems involving partial differential equations
Preprint Number:944
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