A GPU-accelerated adaptive FSAI preconditioner for massively parallel simulations

TL;DR

This paper presents a GPU-accelerated adaptive FSAI preconditioner that significantly improves the efficiency of solving large-scale linear systems in parallel computing environments.

Contribution

It introduces a novel implementation of adaptive FSAI preconditioning on distributed GPU systems, enhancing performance for massive linear algebra problems.

Findings

Outperforms traditional preconditioners in numerical experiments.

Achieves near-ideal behavior in challenging linear algebra problems.

Demonstrates effective parallelism on GPU-accelerated distributed systems.

Abstract

The solution of linear systems of equations is a central task in a number of scientific and engineering applications. In many cases the solution of linear systems may take most of the simulation time thus representing a major bottleneck in the further development of scientific and technical software. For large scale simulations, nowadays accounting for several millions or even billions of unknowns, it is quite common to resort to preconditioned iterative solvers for exploiting their low memory requirements and, at least potential, parallelism. Approximate inverses have been shown to be robust and effective preconditioners in various contexts. In this work, we show how adaptive FSAI, an approximate inverse characterized by a very high degree of parallelism, can be successfully implemented on a distributed memory computer equipped with GPU accelerators. Taking advantage of GPUs in adaptive FSAI set-up is not a trivial task, nevertheless we show through an extensive numerical experimentation how the proposed approach outperforms more traditional preconditioners and results in a close-to-ideal behaviour in challenging linear algebra problems.