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Multiscale modeling in micromagnetics: existence of solutions and numerical integration. (English) Zbl 1320.35336

In this work, the authors prove that under certain assumptions on the nonlinear material law, this multiscale version of the Landau-Lifshitz-Gilbert equation admits weak solutions. The given proof is constructive in the sense that one provides a linear-implicit numerical integrator for the multiscale model such that the numerically computable finite element solutions admit weak \(H^1\)-convergence (at least for a subsequence) towards a weak solution.

MSC:

35Q60 PDEs in connection with optics and electromagnetic theory
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
78M15 Boundary element methods applied to problems in optics and electromagnetic theory
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