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Computing the demagnetizing tensor for finite difference micromagnetic simulations via numerical integration

Computing the demagnetizing tensor for finite difference micromagnetic simulations via numerical integration
Computing the demagnetizing tensor for finite difference micromagnetic simulations via numerical integration
In the finite difference method which is commonly used in computational micromagnetics, the demagnetizing field is usually computed as a convolution of the magnetization vector field with the demagnetizing tensor that describes the magnetostatic field of a cuboidal cell with constant magnetization. An analytical expression for the demagnetizing tensor is available, however at distances far from the cuboidal cell, the numerical evaluation of the analytical expression can be very inaccurate. Due to this large-distance inaccuracy numerical packages such as OOMMF compute the demagnetizing tensor using the explicit formula at distances close to the originating cell, but at distances far from the originating cell a formula based on an asymptotic expansion has to be used. In this work, we describe a method to calculate the demagnetizing field by numerical evaluation of the multidimensional integral in the demagnetizing tensor terms using a sparse grid integration scheme. This method improves the accuracy of computation at intermediate distances from the origin. We compute and report the accuracy of (i) the numerical evaluation of the exact tensor expression which is best for short distances, (ii) the asymptotic expansion best suited for large distances, and (iii) the new method based on numerical integration, which is superior to methods (i) and (ii) for intermediate distances. For all three methods, we show the measurements of accuracy and execution time as a function of distance, for calculations using single precision (4-byte) and double precision (8-byte) floating point arithmetic. We make recommendations for the choice of scheme order and integrating coefficients for the numerical integration method (iii)
0304-8853
440-445
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 (2015) Computing the demagnetizing tensor for finite difference micromagnetic simulations via numerical integration. Journal of Magnetism and Magnetic Materials, 381, 440-445. (doi:10.1016/j.jmmm.2015.01.013).

Record type: Article

Abstract

In the finite difference method which is commonly used in computational micromagnetics, the demagnetizing field is usually computed as a convolution of the magnetization vector field with the demagnetizing tensor that describes the magnetostatic field of a cuboidal cell with constant magnetization. An analytical expression for the demagnetizing tensor is available, however at distances far from the cuboidal cell, the numerical evaluation of the analytical expression can be very inaccurate. Due to this large-distance inaccuracy numerical packages such as OOMMF compute the demagnetizing tensor using the explicit formula at distances close to the originating cell, but at distances far from the originating cell a formula based on an asymptotic expansion has to be used. In this work, we describe a method to calculate the demagnetizing field by numerical evaluation of the multidimensional integral in the demagnetizing tensor terms using a sparse grid integration scheme. This method improves the accuracy of computation at intermediate distances from the origin. We compute and report the accuracy of (i) the numerical evaluation of the exact tensor expression which is best for short distances, (ii) the asymptotic expansion best suited for large distances, and (iii) the new method based on numerical integration, which is superior to methods (i) and (ii) for intermediate distances. For all three methods, we show the measurements of accuracy and execution time as a function of distance, for calculations using single precision (4-byte) and double precision (8-byte) floating point arithmetic. We make recommendations for the choice of scheme order and integrating coefficients for the numerical integration method (iii)

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Accepted/In Press date: 7 January 2015
Published date: 1 May 2015
Organisations: Computational Engineering & Design Group

Identifiers

Local EPrints ID: 381812
URI: https://eprints.soton.ac.uk/id/eprint/381812
ISSN: 0304-8853
PURE UUID: 1710c5c1-7cef-4dbd-9eb3-c9bbd2fb528a

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Date deposited: 16 Oct 2015 08:23
Last modified: 29 Nov 2018 17:31

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