An efficient multigrid preconditioner for Maxwell's equations in micromagnetism

Authors:
ubomír Baňas
Affiliations:
Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, United Kingdom
Venue:
Mathematics and Computers in Simulation
Year:
2010

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Abstract

We consider a system of Maxwell's and Landau-Lifshitz-Gilbert equations describing magnetization dynamics in micromagnetism. The problem is discretized by a convergent, unconditionally stable finite element method. A multigrid preconditioned Uzawa type method for the solution of the algebraic system resulting from the discretized Maxwell's equations is constructed. The efficiency of the method is demonstrated on numerical experiments and the results are compared to those obtained by simplified models.