We report on the design, verification and performance of MuMax3, an open-source GPU-accelerated micromagnetic simulation program. This software solves the time- and space dependent magnetization evolution in nano- to micro scale magnets using a finite-difference discretization. Its high performance and low memory requirements allow for large-scale simulations to be performed in limited time and on inexpensive hardware. We verified each part of the software by comparing results to analytical values where available and to micromagnetic standard problems. MuMax3 also offers specific extensions like MFM image generation, moving simulation window, edge charge removal and material grains.

In the last twenty years, numerical modeling has become an indispensable part of magnetism research. It has become a standard tool for both the exploration of new systems and for the interpretation of experimental data. In the last five years, the capabilities of micromagnetic modeling have dramatically increased due to the deployment of graphical processing units (GPU), which have sped up calculations to a factor of 200. This has enabled many studies which were previously unfeasible. In this topical review, we give an overview of this modeling approach and show how it has contributed to the forefront of current magnetism research.

Thermal fluctuations play an increasingly important role in micromagnetic research relevant for various biomedical and other technological applications. Until now, it was deemed necessary to use a time stepping algorithm with a fixed time step in order to perform micromagnetic simulations at nonzero temperatures. However, Berkov and Gorn have shown in [D. Berkov and N. Gorn, J. Phys.: Condens. Matter,14, L281, 2002] that the drift term which generally appears when solving stochastic differential equations can only influence the length of the magnetization. This quantity is however fixed in the case of the stochastic Landau-Lifshitz-Gilbert equation. In this paper, we exploit this fact to straightforwardly extend existing high order solvers with an adaptive time stepping algorithm. We implemented the presented methods in the freely available GPU-accelerated micromagnetic software package MuMax³ and used it to extensively validate the presented methods. Next to the advantage of having control over the error tolerance, we report a twenty fold speedup without a loss of accuracy, when using the presented methods as compared to the hereto best practice of using Heun’s solver with a small fixed time step.

Micromagnetic simulations are a valuable tool to increase our understanding of nanomagnetic systems and to guide experiments through parameter spaces that would otherwise be difficult and expensive to navigate. To fulfill this task, simulations have always pushed the limits of what is possible in terms of software and hardware. In this perspective, we give an overview of the current state of the art in micromagnetic simulations of ferromagnetic materials followed by our opinion of what tomorrow’s simulations will look like. Recently, the focus has shifted away from exclusively trying to achieve faster simulations, toward extending pure micromagnetic calculations to a multiphysics approach. We present an analysis of how the performance of the simulations is affected by the simulation details and hardware specifications (specific to the graphics processing unit-accelerated micromagnetic software package mumax${}^3$ ), which sheds light on how micromagnetic simulations can maximally exploit the available computational power. Finally, we discuss how micromagnetic simulations can benefit from new hardware paradigms like graphics cards aimed at machine learning.