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A numerical scheme for a Maxwell–Landau–Lifshitz–Gilbert system. (English) Zbl 1099.78020

The aim of this paper is to present two approximation schemes for the time discretization of the Maxwell–Landau–Lifshitz–Gilbert system. Accordingly, two appropriate algorithms (linear and nonlinear) for the computation of the vector field are developed in the paper. The authors justify that the modulus of magnetization is conserved in both cases. Assuming that the electromagnetic field is smooth enough, the error estimates for both approximation schemes is deduced. The paper ends with a numerical example that illustrates the efficiency of the algorithms.

MSC:

78M25 Numerical methods in optics (MSC2010)
78A25 Electromagnetic theory (general)
35Q60 PDEs in connection with optics and electromagnetic theory
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