Experimental Evaluation of Multiprecision Strategies for GMRES on GPUs

TL;DR

This paper investigates multiprecision strategies to accelerate GMRES iterative solvers on GPUs, balancing lower precision performance benefits with the need for double precision accuracy in scientific computing.

Contribution

It introduces methods for integrating multiple precisions into GMRES, including iterative refinement and preconditioners, with strategies for effective multiprecision solver deployment.

Findings

Multiprecision GMRES can significantly improve performance on GPUs.

Optimized low-level kernels further enhance multiprecision solver efficiency.

Strategies for choosing when and how to use multiprecision are proposed.

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 multiprecision 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 multiprecision strategies for accelerating this kernel on GPUs. 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 multiprecision GMRES will be effective and to choose parameters for a multiprecision 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 multiprecision approaches and demonstrate even further improvements are possible by optimizing low-level kernels.