The scalability of a the new ED technique is illustrated (vertical axus: time (s.) to solution, horizontal axis: number of cores). Perfect scalability would be a line with slope -1 on this log-log graph. In fact, the actual performance results are only slightly off the optimal scalability.
Dr. Sergei Isakov, a research scientist at the ETH Institute of Theoretical Physics, is investigating new approaches to look at the behavior of interacting systems known as quantum spin models. The underlying numerical kernel is the determination of a small number of eigenvalues by way of the Exact Diagonalization (ED) technique. This problem has typically proved difficult to parallelize on very large machine configurations.
As part of the High Performance and Productivity Computing (HP2C) initiative, Dr. Isakov and Prof. Matthias Troyer conceived an approach which makes use of data locality, that is, in which each computational process need only communicate with a relatively small number of neighbors through the Message Passing Interface (MPI). This technique maps well to Cray XE6 “Rosa” nodes. Within each node, further parallelism can be achieved by so-called shared-memory (or “OpenMP”) parallelism.
The combination of both MPI and OpenMP parallelism in this new technique means that the ED code will scale to very large machine configurations. After the recent upgrade of Rosa, CSCS scientists had the opportunity to evaluate the ED code on nearly the full machine (up to 47232 cores). The results (see figure) clearly show the scalability of the technique.
The results indicate that larger lattice sizes can be investigated when large machine configurations are used which, in turn, enables new science.
More details on the HP2C initiative can be found at www.hp2c.ch.