A communication reduction approach to iteratively solve large sparse linear systems on a GPGPU cluster

Abstract

Finite Element Methods (FEM) are widely used in academia and industry, especially in the fields of mechanical engineering, civil engineering, aerospace, and electrical engineering. These methods usually convert partial difference equations into large sparse linear systems. For complex problems, solving these large sparse linear systems is a time consuming process. This paper presents a parallelized iterative solver for large sparse linear systems implemented on a GPGPU cluster. Traditionally, these problems do not scale well on GPGPU clusters. This paper presents an approach to reduce the communications between cluster compute nodes for these solvers. Additionally, computation and communication are overlapped to reduce the impact of data exchange. The parallelized system achieved a speedup of up to 15.3 times on 16 NVIDIA Tesla GPUs, compared to a single GPU. An analytical evaluation of the algorithm is conducted in this paper, and the analytical equations for predicting the performance are presented and validated.