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

[摘要] 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 H-2 type, we show that the memory requirements of this FEM/BEM method can be reduced dramatically, effectively converting the quadratic complexity 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 H-2-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.

[发布日期] 2019-05-01

[效力级别]  Proceedings Paper

[关键词] Magnetostatics;Boundary element method;Hierarchical matrix;Micromagnetism