Shape Sensitivities for an Inverse Problem in Magnetic Induction Tomography Based on the Eddy Current Model

In this paper the shape derivative of an objective depending on the solution of an eddy current approximation of Maxwell’s equations is obtained. Using a Lagrangian approach in the spirit of Delfour and Zolésio, the computation of the shape derivative of the solution of the state equation is bypassed. This theoretical result is applied to magnetic impedance tomography, which is an imaging modality aiming at the contactless mapping (identification) of the unknown electrical conductivities inside an object given measurements recorded by receiver coils.Peer Reviewe

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

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

State-constrained optimal control of semilinear elliptic equations with nonlocal radiation interface conditions

We consider a control- and state-constrained optimal control problem governed by a semilinear elliptic equation with nonlocal interface conditions. These conditions occur during the modeling of diffuse-gray conductive-radiative heat transfer. The nonlocal radiation interface condition and the pointwise state constraints represent the particular features of this problem. To deal with the state constraints, continuity of the state is shown, which allows us to derive first-order necessary conditions. Afterwards, we establish second-order sufficient conditions that account for strongly active sets and ensure local optimality in an $L^2$-neighborhood