  Magnetic domain wall motion is at the heart of new magneto-electronic
technologies and hence the need for a deeper understanding of domain wall
dynamics in magnetic systems. In this context, numerical simulations using
simple models can capture the main ingredients responsible for the complex
observed domain wall behavior. We present a scalar-field model for the
magnetization dynamics of quasi-two-dimensional systems with a perpendicular
easy axis of magnetization which allows a direct comparison with typical
experimental protocols, used in polar magneto-optical Kerr effect microscopy
experiments. We show that the thermally activated creep and depinning regimes
of domain wall motion can be reached, and the effect of different quenched
disorder implementations can be assessed with the model. In particular, we show
that the depinning field increases with the mean grain size of a Voronoi
tessellation model for the disorder.
