A numerical scheme for a Maxwell–Landau–Lifshitz–Gilbert system

摘要

We consider Maxwell's equations together with a nonlinear dissipative magnetic law described by the Landau–Lifshitz–Gilbert equation. The paper is devoted to the numerical study of this problem. We introduce two algorithms for the time discretization. The modulus of magnetization is conserved in both cases. Assuming a sufficiently smooth electromagnetic field, we derive the error estimates for both approximation schemes.