Preconditioned nonlinear conjugate gradient method for micromagnetic energy minimization

TL;DR

This paper introduces a sparse preconditioner for a nonlinear conjugate gradient method that significantly accelerates the computation of demagnetization curves in magnetic materials, making simulations more efficient.

Contribution

It presents a novel sparse preconditioner based on the Hessian approximation that improves the speed of energy minimization in micromagnetic simulations.

Findings

Speedup by a factor of 3 for soft magnetic materials

Speedup by a factor of 7 for hard magnetic materials

Computational time scales almost linearly with problem size

Abstract

Fast computation of demagnetization curves is essential for the computational design of soft magnetic sensors or permanent magnet materials. We show that a sparse preconditioner for a nonlinear conjugate gradient energy minimizer can lead to a speed up by a factor of 3 and 7 for computing hysteresis in soft magnetic and hard magnetic materials, respectively. As a preconditioner an approximation of the Hessian of the Lagrangian is used, which only takes local field terms into account. Preconditioning requires a few additional sparse matrix vector multiplications per iteration of the nonlinear conjugate gradient method, which is used for minimizing the energy for a given external field. The time to solution for computing the demagnetization curve scales almost linearly with problem size.