I. Honkonen

Multi-GPU simulations of Vlasov's equation using Vlasiator

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 Earths 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.

Topology aware process mapping

A parallel program based on the Message Passing Interface (MPI) commonly uses point-to-point communication for updating data between processes, and its scalability is ultimately limited by communication costs. To minimize these costs we have developed a library that reduces network congestion, and thus improves performance, by optimizing the placement of processes onto nodes allocated to the parallel job. Our approach is useful on production machines, as irregular communication patterns can at run-time be optimally placed on non-contiguous node allocations. It is also portable as it supports multiple architectures: Cray XT, IBM BlueGene/P and regular SMP clusters. We demonstrate on a Cray XT5m and an Infiniband cluster that good placement of processes doubles the total bandwidth compared to random placement and, furthermore, by up to a factor of 1.4 compared to to the original placement. It is not only important to place processes well on individual nodes, minimizing the number of link traversals on the Cray XT5m provides up to 20 % of additional performance. The scalability of a real-world application, Vlasiator, is also investigated and the scalability is shown to improve by up to 35 %. For communication limited applications the approach provides an avenue to improve performance, and is useful even with dynamic load balancing as the placement is optimized at run-time.