Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large-scale magnetostatic field calculation in finite element
  micromagnetics with H2-matrices   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 & Koehler involves a densely populated matrix with unacceptable
numerical costs for problems involving a large number of degrees of freedom
$N$. By using hierarchical matrices of $\mathcal{H}^2$ type, we show that the
memory requirements for the FEM/BEM method can be reduced dramatically,
effectively converting the quadratic complexity $\mathcal{O}(N^2)$ of the
problem to a linear one $\mathcal{O}(N)$. We obtain matrix size reductions of
nearly $99\%$ in test cases with more than $10^6$ degrees of freedom, and we
test the computed magnetostatic energy values by means of comparison with
analytic values. The efficiency of the $\mathcal{H}^2$-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.

37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom