An inverse scattering problem for the time-dependent Maxwell equations: nonlinear optimization and model-order reduction

SUMMARY In this paper an inverse scattering problem for the time-dependent Maxwell curl equations is considered. This problem is formulated as an optimal control problem governed by partial differential equations. First-order necessary optimality conditions are discussed. For the numerical solution a gradient-based algorithm is applied and successfully tested for some numerical examples. Finally, model-order reduction based on proper orthogonal decomposition is utilized to derive a reduced-order model for the time-dependent Maxwell curl equations. Its applicability is tested with respect to different input frequencies.