Improving the Performance of Dynamical Simulations Via Multiple Right-Hand Sides

This paper presents an algorithmic approach for improving the performance of many types of stochastic dynamical simulations. The approach is to redesign existing algorithms that use sparse matrix-vector products (SPMV) with single vectors to instead use a more efficient kernel, the generalized SPMV (GSPMV), which computes with multiple vectors simultaneously. In this paper, we show how to redesign a dynamical simulation to exploit GSPMV in way that is not initially obvious because only one vector is available at a time. We study the performance of GSPMV as a function of the number of vectors, and demonstrate the use of GSPMV in the Stokesian dynamics method for the simulation of the motion of macromolecules in the cell. Specifically, for our application, we find that with modern multicore Intel microprocessors in clusters of up to 64 nodes, we can typically multiply by 8 to 16 vectors in only twice the time required to multiply by a single vector. After redesigning the Stokesian dynamics algorithm to exploit GSPMV, we measure a 30 percent speedup in performance in single-node, data parallel simulations.