Time-harmonic electromagnetics with exact controllability and discrete exterior calculus

Abstract

In this paper, we apply the exact controllability concept for time-harmonic electromagnetic scattering. The problem is presented in terms of the differential forms, and the discrete exterior calculus is utilized for spatial discretization. Accordingly, the physical properties of the problem are maintained. Despite we consider time-harmonic problems, we concentrate on transient wave equations treated by the exact controllability approach. Essentially, we use a controlled variation of the asymptotic approach with periodic constraints, in which the time-dependent equation is simulated in time, until the time-harmonic solution is reached.