Speeding Up Micromagnetic Simulation by Energy Minimization With Interpolation of Magnetostatic Field

Micromagnetics of rare-earth efficient permanent magnets

“…The magnetization always reaches metastable equilibrium before a significant change of the external field. Based on this argument many researchers use energy minimization methods for simulation of magnetization reversal in permanent magnets, taking advantage of a significant speedup as compared to time integration solvers [11,15]. Minimizing equation ( 16) subject to the unit norm constraint for decreasing external field gives the magnetic states along the demagnetization curve of the magnet.…”

“…In order to reduce the number of energy evaluations Koehler and Fredkin [59] apply an inexact line search based on cubic interpolation. Tanaka and co-workers [15] propose to interpolate the magnetostatic field within the search interval if it is sufficiently small. Fischbacher et al [14] showed that long steps should be avoided, in order to compute all metastable states along the demagnetization curve.…”

“…Micromagnetic simulations are an important tool to understand coercivity mechanisms in permanent magnets. With the advance of hardware for parallel computing [11][12][13] and the improvement of numerical methods [14][15][16], micromagnetic simulations can take into account the microstructure of the magnet and thus help to understand how the interplay between intrinsic magnetic properties and microstructure impacts coercivity.…”

Preconditioned nonlinear conjugate gradient method for micromagnetic energy minimization

“…As a consequence fast solvers for computing the demagnetization curve are required. The computation of the demagnetization curve by minimization of the total energy for subsequent external fields [13,2,47] has proven to be faster than the solution of the dynamical system according to the Landau-Lifshitz Gilbert equation. Micromagnetic solvers based on energy minimization are also the key building blocks for computing the minimum energy path with the string method [5,2,17].…”

“…Accelerated steepest descent methods, which were originally developed for color image denoising [23], were used for the simulation of permanent magnets with a finite element scheme [13] and for the simulation of sensor elements with finite difference [1]. The conjugate gradient method was used for the simulation of soft magnetic elements [27] and permanent magnets [18,47]. Garcia-Cervera [21] and Escobar [2] discussed a truncated Newton method for minimizing the micromagnetic energy.…”