Abstract
In this paper, we develop an optimal control problem to optimize the permittivity and permeability of the metamaterial which can have the invisible cloaking effect. The inverse problem is calibrated as an optimization problem constrained by the time-harmonic Maxwell’s equations. Proper objective functional is introduced with coefficients of the Maxwell’s equations as control variables. We adopt the discontinuous Galerkin method to solve the state equation. Several two-dimensional cloaking benchmark problems are used to test our optimal control method. Numerical results demonstrate that the optimized permittivity and permeability of the metamaterial can achieve the cloaking effectively.
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