A Sparse Symmetric Indefinite Direct Solver for GPU Architectures

Abstract

In recent years, there has been considerable interest in the potential for graphics processing units (GPUs) to speed up the performance of sparse direct linear solvers. Efforts have focused on symmetric positive-definite systems for which no pivoting is required, while little progress has been reported for the much harder indefinite case. We address this challenge by designing and developing a sparse symmetric indefinite solver SSIDS. This new library-quality LDL T factorization is designed for use on GPU architectures and incorporates threshold partial pivoting within a multifrontal approach. Both the factorize and the solve phases are performed using the GPU. Another important feature is that the solver produces bit-compatible results. Numerical results for indefinite problems arising from a range of practical applications demonstrate that, for large problems, SSIDS achieves performance improvements of up to a factor of 4.6 × compared with a state-of-the-art multifrontal solver on a multicore CPU.