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.
Mots-clés : PDE-constrained optimization, electromagnetic induction heating, 3D time-variant heat equations, time-harmonic eddy current equations, pointwise state constraints, optimality conditions
@article{M2AN_2012__46_4_709_0,
author = {Tr\"oltzsch, Fredi and Yousept, Irwin},
title = {PDE-constrained optimization of time-dependent {3D} electromagnetic induction heating by alternating voltages},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {709--729},
publisher = {EDP-Sciences},
volume = {46},
number = {4},
year = {2012},
doi = {10.1051/m2an/2011052},
mrnumber = {2891467},
zbl = {1288.78040},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2011052/}
}
TY - JOUR AU - Tröltzsch, Fredi AU - Yousept, Irwin TI - PDE-constrained optimization of time-dependent 3D electromagnetic induction heating by alternating voltages JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2012 SP - 709 EP - 729 VL - 46 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2011052/ DO - 10.1051/m2an/2011052 LA - en ID - M2AN_2012__46_4_709_0 ER -
%0 Journal Article %A Tröltzsch, Fredi %A Yousept, Irwin %T PDE-constrained optimization of time-dependent 3D electromagnetic induction heating by alternating voltages %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 709-729 %V 46 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2011052/ %R 10.1051/m2an/2011052 %G en %F M2AN_2012__46_4_709_0
Tröltzsch, Fredi; Yousept, Irwin. PDE-constrained optimization of time-dependent 3D electromagnetic induction heating by alternating voltages. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 4, pp. 709-729. doi : 10.1051/m2an/2011052. http://www.numdam.org/articles/10.1051/m2an/2011052/
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