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In this paper we are interested in the numerical modeling of absorbing ferromagnetic materials obeying the non-linear Landau-Lifchitz-Gilbert law with respect to the propagation and scattering of electromagnetic waves. In this work we consider the 1D problem. We rst show that the corresponding Cauchy problem has a unique global solution. We then derive a… (More)

Our goal in this work is to establish the existence and the uniqueness of a smooth solution to what we call in this paper the corner problem, that is to say, the wave equation together with absorbing conditions at two orthogonal boundaries. First we set the existence of a very smooth solution to this initial boundary value problem. Then we show the decay in… (More)

- Peter Monk, Olivier Vacus
- 1997

We propose a nite element method for approximating the non-linear equations describing the electromagnetic eld in a ferromagnetic material. Using energy arguments, we prove an optimal convergence rate for the method assuming a suuciently smooth electromagnetic eld. We also verify that the nite element solution satisses various conservation conditions… (More)

In this paper we consider Maxwell's equations together with a dissipative non-linear magnetic law, the Landau-Lifchitz-Gilbert equation, and we study long time asymptotics of solutions in the 1D case in an innnite domain of propagation. We prove long-time convergence to zero of the electromagnetic eld in a Fr echet topology deened by local energy seminorms:… (More)

We introduce a new algebraic framework to derive discrete absorbing boundary conditions for wave equation in the monodimensional case. The idea is to factor directly the discrete wave operator and then use one of the factors as boundary condition. We also analyse the stability of the schemes obtained this way and perform numerical simulations to estimate… (More)

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