  We consider a lowest-order finite element discretization of the nonlinear
system of Maxwell's and Landau-Lifshitz-Gilbert equations (MLLG). Two
algorithms are proposed to numerically solve this problem, both of which only
require the solution of at most two linear systems per timestep. One of the
algorithms is fully decoupled in the sense that each timestep consists of the
sequential computation of the magnetization and afterwards the magnetic and
electric field. Under some mild assumptions on the effective field, we show
that both algorithms converge towards weak solutions of the MLLG system.
Numerical experiments for a micromagnetic benchmark problem demonstrate the
performance of the proposed algorithms.
