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Computation of the magnetostatic interaction between linearly magnetized polyhedrons

Computation of the magnetostatic interaction between linearly magnetized polyhedrons
Computation of the magnetostatic interaction between linearly magnetized polyhedrons
In this paper we present a method to accurately compute the energy of the magnetostatic interaction between linearly (or uniformly, as a special case) magnetized polyhedrons. The method has applications in finite element micromagnetics, or more generally in computing the magnetostatic interaction when the magnetization is represented using the finite element method (FEM).

The magnetostatic energy is described by a six-fold integral that is singular when the interaction regions overlap, making direct numerical evaluation problematic. To resolve the singularity, we evaluate four of the six iterated integrals analytically resulting in a 2d integral over the surface of a polyhedron, which is nonsingular and can be integrated numerically. This provides a more accurate and efficient way of computing the magnetostatic energy integral compared to existing approaches.

The method was developed to facilitate the evaluation of the demagnetizing interaction between neighbouring elements in finite-element micromagnetics and provides a possibility to compute the demagnetizing field using efficient fast multipole or tree code algorithms.
0304-8853
132-137
Chernyshenko, Dmitri
62dad926-c42a-43db-9312-2cacbd53a042
Fangohr, Hans
9b7cfab9-d5dc-45dc-947c-2eba5c81a160
Chernyshenko, Dmitri
62dad926-c42a-43db-9312-2cacbd53a042
Fangohr, Hans
9b7cfab9-d5dc-45dc-947c-2eba5c81a160

Chernyshenko, Dmitri and Fangohr, Hans (2016) Computation of the magnetostatic interaction between linearly magnetized polyhedrons. Journal of Magnetism and Magnetic Materials, 412 (15), 132-137. (doi:10.1016/j.jmmm.2016.03.083).

Record type: Article

Abstract

In this paper we present a method to accurately compute the energy of the magnetostatic interaction between linearly (or uniformly, as a special case) magnetized polyhedrons. The method has applications in finite element micromagnetics, or more generally in computing the magnetostatic interaction when the magnetization is represented using the finite element method (FEM).

The magnetostatic energy is described by a six-fold integral that is singular when the interaction regions overlap, making direct numerical evaluation problematic. To resolve the singularity, we evaluate four of the six iterated integrals analytically resulting in a 2d integral over the surface of a polyhedron, which is nonsingular and can be integrated numerically. This provides a more accurate and efficient way of computing the magnetostatic energy integral compared to existing approaches.

The method was developed to facilitate the evaluation of the demagnetizing interaction between neighbouring elements in finite-element micromagnetics and provides a possibility to compute the demagnetizing field using efficient fast multipole or tree code algorithms.

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Accepted/In Press date: 28 March 2016
e-pub ahead of print date: 31 March 2016
Published date: 15 August 2016
Organisations: Computational Engineering & Design Group

Identifiers

Local EPrints ID: 391926
URI: https://eprints.soton.ac.uk/id/eprint/391926
ISSN: 0304-8853
PURE UUID: ce79b517-b523-4062-a7fb-a03d4afdb00f

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Date deposited: 13 Apr 2016 13:12
Last modified: 29 Nov 2018 17:31

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