Graphics Processing Unit Accelerated $O(N)$ Micromagnetic Solver

An efficient micromagnetic solver running on graphics processing units (GPU) is demonstrated. The solver implements a nonuniform grid interpolation method (NGIM) to compute the superposition integral for the magnetostatic field with operations and memory requirements. The NGIM divides the computational domain into a hierarchy of boxes containing sources and observers, and it uses spatial interpolation from sparse nonuniform grids to achieve computational savings. Efficiency of the GPU solver is achieved by using coalesced memory accessing requiring arranging data in contiguous addresses, one-block-per-box computations with a block of threads handling an observation box to achieve the best utilization of the GPU threads, and on-fly computation of all grids and interpolation coefficients leading to reduced memory and increased speed. The GPU-CPU speed-ups are shown to be in the range 40-100 depending on the problem size and accuracy. A simple and inexpensive GPU is shown to handle efficiently problems comprising discretizations of more than 16 million of spins.