Exact boundary controllability of the second-order Maxwell system: Theory and numerical simulation

The exact controllability of the second order time-dependent Maxwell equations for the electric field is addressed through the Hilbert Uniqueness Method. A two-grid preconditioned conjugate gradient algorithm is employed to inverse the H.U.M. operator and to construct the numerical control. The underlying initial value problems are discretized by Lagrange finite elements and an implicit Newmark scheme. Two-dimensional numerical experiments illustrate the performance of the method.