Parallelizing Kernel Polynomial Method Applying Graphics Processing Units

Abstract

The Kernel Polynomial Method (KPM) is one of the fast diagonalization methods used for simulations of quantum systems in research fields of condensed matter physics and chemistry. The algorithm has a difficulty to be parallelized on a cluster computer or a supercomputer due to the fine-grain recursive calculations. This paper proposes an implementation of the KPM on the recent graphics processing units (GPU) where the recursive calculations are able to be parallelized in the massively parallel environment. This paper also describes performance evaluations regarding the cases when the actual simulation parameters are applied, where one parameter is applied for the increased intensive calculations and another is applied for the increased amount of memory usage. Moreover, the impact for applying the Compress Row Storage (CRS) format to the KPM algorithm is also discussed. Finally, it concludes that the performance on the GPU promises very high performance compared to the one on CPU and reduces the overall simulation time.