Improving the Performance of the Sparse Matrix Vector Product with GPUs

Abstract

Sparse matrices are involved in linear systems, eigensystems and partial differential equations from a wide spectrum of scientific and engineering disciplines. Hence, sparse matrix vector product (SpMV) is considered as key operation in engineering and scientific computing. For these applications the optimization of the sparse matrix vector product (SpMV) is very relevant. However, the irregular computation involved in SpMV prevents the optimum exploitation of computational architectures when the sparse matrices are very large. Graphics Processing Units (GPUs) have recently emerged as platforms that yield outstanding acceleration factors. SpMV implementations for GPUs have already appeared on the scene. This work proposes and evaluates new implementations of SpMV for GPUs called ELLR-T. They are based on the format ELLPACK-R, which allows storage of the sparse matrix in a regular manner. A comparative evaluation against a variety of storage formats previously proposed has been carried out based on a representative set of test matrices. The results show that: (1) the SpMV is highly accelerated with GPUs; (2) the performance strongly depends on the specific pattern of the matrix; and (3) the implementations ELLR-T achieve higher overall performance. Consequently, the new implementations of SpMV, ELLR-T, described in this paper can help to exploit the GPUs, because, they achieve high performance and they can be easily joined in the engineering and scientific computing.