Convergence of a mass-lumped finite element method for the Landau-Lifshitz equation
| Autor: | Jon Wilkening, Eugenia Kim |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Physics
Applied Mathematics Weak solution Mathematical analysis Numerical Analysis (math.NA) 010103 numerical & computational mathematics Unit square 01 natural sciences Finite element method Landau–Lifshitz–Gilbert equation 010101 applied mathematics Dispersive partial differential equation Nonlinear system FOS: Mathematics Periodic boundary conditions Mathematics - Numerical Analysis 0101 mathematics Micromagnetics |
| Zdroj: | Quarterly of Applied Mathematics. 76:383-405 |
| ISSN: | 1552-4485 0033-569X |
| DOI: | 10.1090/qam/1485 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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