GPU Accelerated Sparse Cholesky Factorization

TL;DR

This paper explores GPU acceleration techniques for sparse Cholesky factorization, significantly reducing computation time for large-scale scientific problems by offloading dense matrix operations to GPUs.

Contribution

It introduces methods for offloading dense matrix operations in sparse Cholesky factorization to GPUs, achieving up to 4x speedup over CPU-only implementations.

Findings

Up to 4x speedup with GPU acceleration

Effective offloading of dense matrix operations

Potential for improved large-scale scientific computations

Abstract

The solution of sparse symmetric positive definite linear systems is an important computational kernel in large-scale scientific and engineering modeling and simulation. We will solve the linear systems using a direct method, in which a Cholesky factorization of the coefficient matrix is performed using a right-looking approach and the resulting triangular factors are used to compute the solution. Sparse Cholesky factorization is compute intensive. In this work we investigate techniques for reducing the factorization time in sparse Cholesky factorization by offloading some of the dense matrix operations on a GPU. We will describe the techniques we have considered. We achieved up to 4x speedup compared to the CPU-only version.