Optimal control of the full time-dependent Maxwell equations (Q2798140)

The paper analyzes the optimal control problem for the time-dependent Maxwell equations. The goal is to find an optimal divergence free current density \({\mathbf u}(x)\) and its time-dependent amplitude \(a(t)\) within a fixed range, which drive the electric and magnetic fields to the desired ones. The key tools for the analysis of the problem are semigroup theory and the Helmholtz decomposition theory. The main theoretical results are existence and regularity of an optimal solution. To solve the nonlinear optimality system the authors use a semismooth Newton algorithm. The paper includes some numerical results where mixed finite elements methods are used for space discretization and the Crank-Nicholson method is used for time discretization.