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...

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...

In this paper we propose a new concept of quasi-uniform monotonicity weaker than the uniform monotonicity which has been developed in the study of nonlinear operator equation $Au=b$. We prove that if $A$ is a quasi-uniformly monotone and hemi-continuous operator, then $A^{-1}$ is strictly monotone, bounded and continuous, and thus the Galerkin approximations converge. Also we show an application of a quasi-uniformly monotone and hemi-continuous operator to the proof of the well-posedness and convergence...

We present a weak parametrix of the operator of the CFIE equation. An interesting feature of this parametrix is that it is compatible with different discretization strategies and hence allows for the construction of efficient preconditioners dedicated to the CFIE. Furthermore, one shows that the underlying operator of the CFIE verifies an uniform discrete Inf-Sup condition which allows to predict an original convergence result of the numerical solution of the CFIE to the exact one.

On exhibe dans cette note une paramétrix (au sens faible) de l'opérateur sous-jacent à l'équation CFIE de l'électromagnétisme. L'intérêt de cette paramétrix est de se prêter à différentes stratégies de discrétisation et ainsi de pouvoir être utilisée comme préconditionneur de la CFIE. On montre aussi que l'opérateur sous-jacent à la CFIE satisfait une condition Inf-Sup discrète uniforme, applicable aux espaces de discrétisation usuellement rencontrés en électromagnétisme, et qui permet d'établir...