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Convergence of a mass-lumped finite element method for the Landau-Lifshitz equation. (arXiv:1608.07312v3 [math.NA] UPDATED)
来源于:arXiv
The dynamics of the magnetic distribution in a ferromagnetic material is
governed by the Landau-Lifshitz equation, which is a nonlinear geometric
dispersive equation with a nonconvex constraint that requires the magnetization
to remain of unit length throughout the domain. In this article, we present a
mass-lumped finite element method for the Landau-Lifshitz equation. This method
preserves the nonconvex constraint at each node of the finite element mesh, and
is energy nonincreasing. We show that the numerical solution of our method for
the Landau-Lifshitz equation converges to a weak solution of the
Landau-Lifshitz-Gilbert equation using a simple proof technique that cancels
out the product of weakly convergent sequences. Numerical tests for both
explicit and implicit versions of the method on a unit square with periodic
boundary conditions are provided for structured and unstructured meshes. 查看全文>>