A Message-Driven, Multi-GPU Parallel Sparse Triangular Solver

Abstract

Sparse triangular solve is used in conjunction with Sparse LU for solving sparse linear systems, either as a direct solver or as a preconditioner. As GPUs have become a firstclass compute citizen, designing an efficient and scalable SpTRSV on multi-GPU HPC systems is imperative. In this paper, we leverage the advantage of GPU-initiated data transfers of NVSHMEM to implement and evaluate a Multi-GPU SpTRSV. We create a novel producer-consumer paradigm to manage the computation and communication in SpTRSV and implement it using two CUDA streams. Our multi-GPU SpTRSV implementation using CUDA streams achieves a 3.7× speedup when using twelve GPUs (two nodes) relative to our implementation on a single GPU, and up to 6.1× compared to cusparse csrsv2() over the range of one to eighteen GPUs. To further explain the observed performance and explore the key features of matrices to estimate the potential performance benefits when using multi-GPU, we extend the critical path model of SpTRSV to GPUs. We demonstrate the ability of our performance model to understand various aspects of performance and performance bottlenecks on multi-GPU and motivate code