Compression of boundary element matrix in micromagnetic simulations

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 × N matrix B i j , 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 i j . An efficient approach is to approximate B i j 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.