A Study of Mixed Precision Strategies for GMRES on GPUs

TL;DR

This paper investigates mixed precision strategies to accelerate GMRES linear solver on GPUs, balancing hardware efficiency with the need for double precision accuracy in scientific computing.

Contribution

It presents new mixed precision methods for GMRES, including iterative refinement and preconditioners, with strategies to optimize their effectiveness on GPU hardware.

Findings

Mixed precision GMRES can significantly improve performance.

Strategies for choosing precision parameters enhance solver efficiency.

Performance portability achieved through Kokkos Kernels.

Abstract

Support for lower precision computation is becoming more common in accelerator hardware due to lower power usage, reduced data movement and increased computational performance. However, computational science and engineering (CSE) problems require double precision accuracy in several domains. This conflict between hardware trends and application needs has resulted in a need for mixed precision strategies at the linear algebra algorithms level if we want to exploit the hardware to its full potential while meeting the accuracy requirements. In this paper, we focus on preconditioned sparse iterative linear solvers, a key kernel in several CSE applications. We present a study of mixed precision strategies for accelerating this kernel on an NVIDIA V$100$ GPU with a Power 9 CPU. We seek the best methods for incorporating multiple precisions into the GMRES linear solver; these include iterative refinement and parallelizable preconditioners. Our work presents strategies to determine when mixed precision GMRES will be effective and to choose parameters for a mixed precision iterative refinement solver to achieve better performance. We use an implementation that is based on the Trilinos library and employs Kokkos Kernels for performance portability of linear algebra kernels. Performance results demonstrate the promise of mixed precision approaches and demonstrate even further improvements are possible by optimizing low-level kernels.