Multi-GPU simulations of Vlasov’s equation using Vlasiator

• We use GPUs to accelerate the propagation of six-dimensional Vlasov equation using a finite volume method.
• The simulation has been parallelized with MPI. CUDA streams were used to pipeline GPU–CPU and CPU–CPU data transfers.
• Presented pipeline strategy simplifies the coding of parallel GPU simulations.

We present a numerical method, based on a three-dimensional finite volume wave-propagation algorithm, for solving the Vlasov equation in a full six-dimensional (three spatial coordinates, three velocity coordinates) case in length scales comparable to the size of the Earth’s magnetosphere. The method uses Strang splitting to separate propagation in spatial and velocity coordinates, and is second-order accurate in spatial and velocity spaces and in time. The method has been implemented on general-purpose graphics processing units for faster computations and has been parallelised using the message passing interface.