Compression of boundary element matrix in micromagnetic simulations

Reference:

Knittel, A., Franchin, M., Bordignon, G., Fischbacher, T., Bending, S. and Fangohr, H., 2009. Compression of boundary element matrix in micromagnetic simulations. Journal of Applied Physics, 105 (7), 07D542.

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Official URL:

http://dx.doi.org/10.1063/1.3072032

Abstract

A hybrid finite element method/boundary element method (FEM/BEM) is a standard approach for calculating the magnetostatic potential within micromagnetics [D. Fredkin and T. Koehler, IEEE Trans. Magn. 26, 415 (1990)]. This involves dealing with a dense N X N matrix B-ij, with N being the number of mesh surface nodes. In order to apply the method to ferromagnetic structures with a large surface, one needs to apply matrix compression techniques on B-ij. An efficient approach is to approximate B-ij by hierarchical matrices (or H matrices). We have used HLIB [http://www.hlib.org], a library containing implementations of the hierarchical matrix methodology, together with the micromagnetic finite element solver NMAG in order to optimize the hybrid FEM/BEM. In this article we present a study of the efficiency of algorithms implemented in HLIB concerning the storage requirements and the matrix assembly time in micromagnetic simulations.

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