21 research outputs found
Shape sensitivities for an inverse problem in magnetic induction tomography based on the eddy current model
Optimal control of quasilinear H(curl)-elliptic partial differential equations in magnetostatic field problems
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
Finite element analysis of an optimal control problem in the coefficients of time-harmonic eddy current equations
Regularization of state-constrained elliptic optimal control problems with nonlocal radiation interface conditions
Optimal Control of Quasilinear -Elliptic Partial Differential Equations in Magnetostatic Field Problems
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 -neighborhood
An extrapolation method for state-constrained optimal control problems
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