Abstract
We propose an implicit, fully discrete scheme for the numerical solution of the Maxwell-Landau-Lifshitz-Gilbert equation which is based on linear finite elements and satisfies a discrete sphere constraint as well as a discrete energy law. As numerical parameters tend to zero, solutions weakly accumulate at weak solutions of the Maxwell-Landau-Lifshitz-Gilbert equation. A practical linearization of the nonlinear scheme is proposed and shown to converge for certain scalings of numerical parameters. Computational studies are presented to indicate finite-time blowup behavior and to study combined electromagnetic phenomena in ferromagnets for benchmark problems. © 2008 Society for Industrial and Applied Mathematics.
Original language | English |
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Pages (from-to) | 1399-1422 |
Number of pages | 24 |
Journal | SIAM Journal on Numerical Analysis |
Volume | 46 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2008 |
Keywords
- Convergence
- Ferromagnetism
- Finite elements
- Maxwell-Landau-Lifshitz-Gilbert equation