An efficient multigrid preconditioner for Maxwell's equations in micromagnetism

Lubomir Banas

doi:10.1016/j.matcom.2009.02.009

An efficient multigrid preconditioner for Maxwell's equations in micromagnetism

Lubomir Banas

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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. © 2009 IMACS.

Original language	English
Pages (from-to)	1657-1663
Number of pages	7
Journal	Mathematics and Computers in Simulation
Volume	80
Issue number	8
DOIs	https://doi.org/10.1016/j.matcom.2009.02.009
Publication status	Published - Apr 2010

Keywords

Ferromagnetism
Finite elements
Maxwell-Landau-Lifshitz-Gilbert equations
Multigrid
Preconditioner

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10.1016/j.matcom.2009.02.009

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title = "An efficient multigrid preconditioner for Maxwell's equations in micromagnetism",

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. {\textcopyright} 2009 IMACS.",

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AU - Banas, Lubomir

PY - 2010/4

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AB - 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. © 2009 IMACS.

KW - Ferromagnetism

KW - Finite elements

KW - Maxwell-Landau-Lifshitz-Gilbert equations

KW - Multigrid

KW - Preconditioner

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U2 - 10.1016/j.matcom.2009.02.009

DO - 10.1016/j.matcom.2009.02.009

M3 - Article

SN - 0378-4754

VL - 80

SP - 1657

EP - 1663

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

IS - 8

ER -

An efficient multigrid preconditioner for Maxwell's equations in micromagnetism

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Keywords

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