# On the performance of various parallel GMRES implementations on CPU and GPU clusters

## TL;DR

This paper compares various parallel GMRES implementations across CPU and GPU clusters, highlighting GPU architectures' high potential for large-scale sparse linear system solutions.

## Contribution

It presents new parallel GMRES implementations optimized for different architectures, including GPU-based systems, and evaluates their performance on a benchmark problem.

## Key findings

- GPU-based implementations show significant speedup over CPU-based ones.
- Memory management issues are critical in parallel GMRES performance.
- GPU architectures demonstrate high potential for large sparse linear system solutions.

## Abstract

As the need for computational power and efficiency rises, parallel systems become increasingly popular among various scientific fields. While multiple core-based architectures have been the center of attention for many years, the rapid development of general purposes GPU-based architectures takes high performance computing to the next level. In this work, different implementations of a parallel version of the preconditioned GMRES - an established iterative solver for large and sparse linear equation sets - are presented, each of them on different computing architectures: From distributed and shared memory core-based to GPU-based architectures. The computational experiments emanate from the dicretization of a benchmark boundary value problem with the finite element method. Major advantages and drawbacks of the various implementations are addressed in terms of parallel speedup, execution time and memory issues. Among others, comparison of the results in the different architectures, show the high potentials of GPU-based architectures.