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We consider control constrained optimal control problems governed byparameterized stationary Maxwell's system with the Gauss's law. The parametersenter through dielectric, magnetic permeability, and charge density. Moreover,the parameter set is assumed to be compact. We discretize the electric field bya finite element method and use variational discretization concept todiscretize the control. We create a reduced basis method for the optimalcontrol problem and establish uniform convergence of the reduced ordersolutions to that of the original high dimensional problem provided that thesnapshot parameter sample is dense in the parameter set, with an appropriateparameter separability rule. Finally, we establish the absolute a posteriorierror estimator for the reduced order solutions and the corresponding costfunctions in terms of the state and adjoint residuals.

Optimal Control of Parameterized Maxwell's System: Reduced Basis, Convergence Analysis, and A Posteriori Error Estimates