Development of Krylov and AMG linear solvers for large-scale sparse matrices on GPUs

TL;DR

This paper presents the development and implementation of Krylov subspace and AMG linear solvers optimized for large-scale sparse matrices on NVIDIA GPUs, including novel algorithms and communication strategies that enhance performance.

Contribution

The work introduces GPU-optimized Krylov and AMG solvers with new algorithms for SpMV, preconditioning, and communication, enabling efficient large-scale sparse matrix solutions.

Findings

Favorable acceleration performance of Krylov and AMG solvers on GPUs

Effective algorithms for SpMV and preconditioning in parallel environments

Implementation of communication mechanisms for multi-GPU scalability

Abstract

This research introduce our work on developing Krylov subspace and AMG solvers on NVIDIA GPUs. As SpMV is a crucial part for these iterative methods, SpMV algorithms for single GPU and multiple GPUs are implemented. A HEC matrix format and a communication mechanism are established. And also, a set of specific algorithms for solving preconditioned systems in parallel environments are designed, including ILU(k), RAS and parallel triangular solvers. Based on these work, several Krylov solvers and AMG solvers are developed. According to numerical experiments, favorable acceleration performance is acquired from our Krylov solver and AMG solver under various parameter conditions.