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

The efficient solution to systems of linear and non-linear 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. There is a common need for efficient implementation and computational performance of solution of sparse system of linear equations in many unstructured finite element-based computations of physics based modeling problems. 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. An unstructured finite element-based computational simulation involving multiple calls to iterative pre-conditioned conjugate gradient algorithm for the solution to a linear system of equations employing a single CPU-GPU computing system using NVidia Compute Unified Device Architecture libraries is employed for the results discussed in the present paper. The matrix-vector product implementation is examined within the context of a resin transfer molding simulation code. Results from the present work can be applied without loss of generality to many other unstructured, finite element-based computational modeling applications in science and engineering that employ solutions to sparse linear and non-linear system of equations using CPU-GPU architecture. 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.