Efficient computation of demagnetising fields for magnetic multilayers using multilayered convolution

As research into magnetic thin films and spintronics devices is moving from single to multiple magnetic layers, there is a need for micromagnetics modelling tools specifically designed to efficiently handle magnetic multilayers. Here we show an exact method of computing demagnetising fields in magnetic multilayers, which is able to handle layers with arbitrary spacing, arbitrary thicknesses, and arbitrary relative positioning between them without impacting on the computational performance, or sacrificing numerical accuracy. The multilayered convolution method is a generalisation of the well-known convolution method used to compute demagnetising fields in a single magnetic body. In typical use cases, such as multilayered stacks used to study skyrmions, we show the multilayered convolution method can be up to 8 times faster, implemented both for central processors and graphics processors, compared to the simple convolution method.