Cost-effective way to speed up micromagnetic simulations in granular media

Abstract

In this paper an investigation of the effect of the maximum dimension of the Krylov subspace projection methods, within the Ordinary Differential Equations (ODEs) context, on the speed of micromagnetic simulations of granular media has been done. The stiffness of the problem has been investigated using two different solvers, a nonstiff (Adams) and a stiff one (backward differentiation formulae, BDF) for the solution of the large system of ODEs. Then micromagnetic simulations have been run for a variety of values of the maximum dimension of the Krylov subspace for different sizes of finite elements in order to establish an optimum value. Adams method requires 3 times more CPU time than BDF for the same simulation time. The latter result shows that granular media micromagnetic simulations are stiff. Furthermore, it has been found that increasing the maximum dimension of the Krylov subspace to 15 (default value =5) a considerable increase to the speed of the simulations occurs in the order of 20–52%.