CUDA GPU libraries and novel sparse matrix-vector multiplication implementation and performance enhancement in unstructured finite element computations

Abstract

The efficient solution to systems of linear and nonlinear equations arising from sparse matrix operations is a ubiquitous challenge for computing applications that can be exacerbated by the employment of heterogeneous architectures such as CPU-GPU computing systems. This paper presents our implementation of a novel sparse matrix-vector multiplication (a significant compute load operation in the iterative solution via pre-conditioned conjugate gradient based methods) employing LightSpMV with compressed sparse row (CSR) format, and the resulting performance characteristics using an unstructured finite element-based computational simulation. Computational performance analysed indicates that LightSpMV can provide an asset to boost performance for these computational modelling applications. This work also investigates potential improvements in the LightSpMV algorithm using CUDA 35 intrinsic, which results in an additional performance boost by 1%. While this may not be significant, it supports the idea that LightSpMV can potentially be used for other full-solution finite element-based computational implementations.