Numerical study of nonlinear ferromagnetic materials

We consider Maxwell's equations together with a nonlinear dissipative magnetic law described by Landau-Lifshitz-Gilbert equation. We suggest two new numerical schemes (linear and nonlinear) for a time discretization of the nonlinear equations describing a quasi-static electromagnetic field in a ferromagnetic material. Both are designed in such a way that they conserve the quantities natural for the continuous model. Assuming a bounded magnetic field we derive the error estimates for both approximation algorithms.

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