A New Sparse Matrix Vector Multiplication GPU Algorithm Designed for Finite Element Problems

TL;DR

This paper introduces a new GPU algorithm for sparse matrix-vector multiplication tailored for finite element problems, demonstrating significant speedups and efficiency improvements over existing methods in various applications.

Contribution

The paper presents a novel GPU-based SPMV algorithm optimized for unstructured finite element meshes, outperforming current algorithms in bandwidth and speed for diverse sparse matrices.

Findings

New algorithms outperform existing GPU SPMV methods in bandwidth.

Speedup factors up to 12 times in finite element simulations.

Effective in real-world finite element applications.

Abstract

Recently, graphics processors (GPUs) have been increasingly leveraged in a variety of scientific computing applications. However, architectural differences between CPUs and GPUs necessitate the development of algorithms that take advantage of GPU hardware. As sparse matrix vector multiplication (SPMV) operations are commonly used in finite element analysis, a new SPMV algorithm and several variations are developed for unstructured finite element meshes on GPUs. The effective bandwidth of current GPU algorithms and the newly proposed algorithms are measured and analyzed for 15 sparse matrices of varying sizes and varying sparsity structures. The effects of optimization and differences between the new GPU algorithm and its variants are then subsequently studied. Lastly, both new and current SPMV GPU algorithms are utilized in the GPU CG Solver in GPU finite element simulations of the heart. These results are then compared against parallel PETSc finite element implementation results. The effective bandwidth tests indicate that the new algorithms compare very favorably with current algorithms for a wide variety of sparse matrices and can yield very notable benefits. GPU finite element simulation results demonstrate the benefit of using GPUs for finite element analysis, and also show that the proposed algorithms can yield speedup factors up to 12-fold for real finite element applications.