A finite element approximation for the quasi-static Maxwell--Landau--Lifshitz--Gilbert equations

Abstract

The quasi-static Maxwell–Landau–Lifshitz–Gilbert equations which describe the electromagnetic behaviour of a ferromagnetic material are highly nonlinear. Sophisticated numerical schemes are required to solve the equations, given their nonlinearity and the constraint that the solution stays on a sphere. We propose an implicit finite element solution to the problem. The resulting system of algebraic equations is linear which facilitates the solution process compared to nonlinear methods. We present numerical results to show the efficacy of the proposed method. References

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