In this paper, an inverse scattering problem for the time-dependent Maxwell curl equations is considered on an unbounded domain. This problem is formulated as an optimal control problem governed by partial differential equations. Utilizing techniques from infinite-dimensional optimization first-order necessary optimality conditions is presented. For the numerical solution, a gradient-based algorithm is successfully applied. To investigate the applicability of reduced-order modeling in the context of the underlying inverse scattering problem, the method of proper orthogonal decomposition is studied for the Maxwell equations with respect to changes in the excitation frequencies and change of parameters. Numerical tests illustrate the efficiency for the proper orthogonal decomposition model-order reduction approach. Copyright © 2013 John Wiley & Sons, Ltd.
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