Geometric space-time integration of ferromagnetic materials

Jason Frank

doi:10.1016/j.apnum.2003.11.003

Geometric space-time integration of ferromagnetic materials

Jason Frank^*

^*Corresponding author for this work

extern

Research output: Contribution to journal › Conference article › Academic › peer-review

Abstract

The Landau-Lifshitz equation (LLE) governing the flow of magnetic spin in a ferromagnetic material is a PDE with a noncanonical Hamiltonian structure. In this paper we derive a number of new formulations of the LLE as a partial differential equation on a multisymplectic structure. Using this form we show that the standard central spatial discretization of the LLE gives a semi-discrete multisymplectic PDE, and suggest an efficient symplectic splitting method for time integration. Furthermore we introduce a new space-time box scheme discretization which satisfies a discrete local conservation law for energy flow, implicit in the LLE, and made transparent by the multisymplectic framework.

Original language	English
Pages (from-to)	307-322
Number of pages	16
Journal	Applied Numerical Mathematics
Volume	48
Issue number	3-4
DOIs	https://doi.org/10.1016/j.apnum.2003.11.003
Publication status	Published - Mar 2004
Externally published	Yes
Event	Workshop on Innovative Time Integrators for PDEs (CWI) - Amsterdam, Netherlands Duration: 25 Nov 2002 → 27 Nov 2002

Keywords

Ferromagnetic materials
Geometric integration
Landau-Lifshitz equation
Multisymplectic structure

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10.1016/j.apnum.2003.11.003

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title = "Geometric space-time integration of ferromagnetic materials",

abstract = "The Landau-Lifshitz equation (LLE) governing the flow of magnetic spin in a ferromagnetic material is a PDE with a noncanonical Hamiltonian structure. In this paper we derive a number of new formulations of the LLE as a partial differential equation on a multisymplectic structure. Using this form we show that the standard central spatial discretization of the LLE gives a semi-discrete multisymplectic PDE, and suggest an efficient symplectic splitting method for time integration. Furthermore we introduce a new space-time box scheme discretization which satisfies a discrete local conservation law for energy flow, implicit in the LLE, and made transparent by the multisymplectic framework.",

keywords = "Ferromagnetic materials, Geometric integration, Landau-Lifshitz equation, Multisymplectic structure",

author = "Jason Frank",

note = "Funding Information: E-mail address: [email protected] (J. Frank). 1 Funding from an NWO Innovative Research Grant is gratefully acknowledged.; Workshop on Innovative Time Integrators for PDEs (CWI) ; Conference date: 25-11-2002 Through 27-11-2002",

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doi = "10.1016/j.apnum.2003.11.003",

language = "English",

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T1 - Geometric space-time integration of ferromagnetic materials

AU - Frank, Jason

N1 - Funding Information: E-mail address: [email protected] (J. Frank). 1 Funding from an NWO Innovative Research Grant is gratefully acknowledged.

PY - 2004/3

Y1 - 2004/3

N2 - The Landau-Lifshitz equation (LLE) governing the flow of magnetic spin in a ferromagnetic material is a PDE with a noncanonical Hamiltonian structure. In this paper we derive a number of new formulations of the LLE as a partial differential equation on a multisymplectic structure. Using this form we show that the standard central spatial discretization of the LLE gives a semi-discrete multisymplectic PDE, and suggest an efficient symplectic splitting method for time integration. Furthermore we introduce a new space-time box scheme discretization which satisfies a discrete local conservation law for energy flow, implicit in the LLE, and made transparent by the multisymplectic framework.

AB - The Landau-Lifshitz equation (LLE) governing the flow of magnetic spin in a ferromagnetic material is a PDE with a noncanonical Hamiltonian structure. In this paper we derive a number of new formulations of the LLE as a partial differential equation on a multisymplectic structure. Using this form we show that the standard central spatial discretization of the LLE gives a semi-discrete multisymplectic PDE, and suggest an efficient symplectic splitting method for time integration. Furthermore we introduce a new space-time box scheme discretization which satisfies a discrete local conservation law for energy flow, implicit in the LLE, and made transparent by the multisymplectic framework.

KW - Ferromagnetic materials

KW - Geometric integration

KW - Landau-Lifshitz equation

KW - Multisymplectic structure

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DO - 10.1016/j.apnum.2003.11.003

M3 - Conference article

AN - SCOPUS:1042263828

SN - 0168-9274

VL - 48

SP - 307

EP - 322

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

IS - 3-4

T2 - Workshop on Innovative Time Integrators for PDEs (CWI)

Y2 - 25 November 2002 through 27 November 2002

ER -

Geometric space-time integration of ferromagnetic materials

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Keywords

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