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

• Volume: 46, Issue: 4, page 709-729
• ISSN: 0764-583X

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## Abstract

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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.

## How to cite

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Tröltzsch, Fredi, and Yousept, Irwin. "PDE-constrained optimization of time-dependent 3D electromagnetic induction heating by alternating voltages." ESAIM: Mathematical Modelling and Numerical Analysis 46.4 (2012): 709-729. <http://eudml.org/doc/276385>.

@article{Tröltzsch2012,
abstract = {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.},
author = {Tröltzsch, Fredi, Yousept, Irwin},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {PDE-constrained optimization; electromagnetic induction heating; 3D time-variant heat equations; time-harmonic eddy current equations; pointwise state constraints; optimality conditions},
language = {eng},
month = {2},
number = {4},
pages = {709-729},
publisher = {EDP Sciences},
title = {PDE-constrained optimization of time-dependent 3D electromagnetic induction heating by alternating voltages},
url = {http://eudml.org/doc/276385},
volume = {46},
year = {2012},
}

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
DA - 2012/2//
PB - EDP Sciences
VL - 46
IS - 4
SP - 709
EP - 729
AB - 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.
LA - eng
KW - PDE-constrained optimization; electromagnetic induction heating; 3D time-variant heat equations; time-harmonic eddy current equations; pointwise state constraints; optimality conditions
UR - http://eudml.org/doc/276385
ER -

## References

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