Large-scale magnetostatic field calculation in finite element micromagnetics with H2-matrices.

Hertel, Riccardo, Christophersen, Sven and Börm, Steffen (2019) Large-scale magnetostatic field calculation in finite element micromagnetics with H2-matrices. Journal of Magnetism and Magnetic Materials, 477 . pp. 118-123. DOI 10.1016/j.jmmm.2018.12.103.

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Abstract

Magnetostatic field calculations in micromagnetic simulations can be numerically expensive, particularly in the case of large-scale finite element simulations. The established finite element/boundary element method (FEM/BEM) by Fredkin and Koehler (1990) involves a densely populated matrix with unacceptable numerical costs for problems with a large number of degrees of freedom N. By using hierarchical matrices of H2 type, we show that the memory requirements of this FEM/BEM method can be reduced dramatically, effectively converting the quadratic complexity O(N2) of the problem to a linear one O(N). We obtain matrix size reductions of nearly 99% in test cases with more than 106 degrees of freedom, and we test the computed magnetostatic energy values by means of comparison with analytic values. The efficiency of the H2-matrix compression opens the way to large-scale magnetostatic field calculations in micromagnetic modeling, all while preserving the accuracy of the established FEM/BEM formalism.

Document Type: Article
Keywords: Magnetostatics, Boundary element method, Hierarchical matrix, Micromagnetism
Research affiliation: Kiel University > Kiel Marine Science
OceanRep > The Future Ocean - Cluster of Excellence > FO-R11
OceanRep > The Future Ocean - Cluster of Excellence
Kiel University
Refereed: Yes
Open Access Journal?: No
DOI etc.: 10.1016/j.jmmm.2018.12.103
ISSN: 0304-8853
Projects: Future Ocean
Date Deposited: 01 Aug 2019 10:52
Last Modified: 02 Jan 2020 12:11
URI: http://oceanrep.geomar.de/id/eprint/47313

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