Parallel Unsmoothed Aggregation Algebraic Multigrid Algorithms on GPUs

TL;DR

This paper presents a parallel algebraic multigrid method tailored for GPUs, utilizing aggregation and a K-cycle iteration with an $$-Jacobi smoother to efficiently solve isotropic graph Laplacian problems.

Contribution

It introduces a GPU-optimized AMG algorithm based on aggregation, featuring a parallel setup and a K-cycle solve phase, demonstrating improved performance for graph Laplacian problems.

Findings

Effective parallel implementation on GPUs.

Demonstrated efficiency in solving graph Laplacian problems.

Utilized aggregation framework with a K-cycle iteration.

Abstract

We design and implement a parallel algebraic multigrid method for isotropic graph Laplacian problems on multicore Graphical Processing Units (GPUs). The proposed AMG method is based on the aggregation framework. The setup phase of the algorithm uses a parallel maximal independent set algorithm in forming aggregates and the resulting coarse level hierarchy is then used in a K-cycle iteration solve phase with a $\ell^1$-Jacobi smoother. Numerical tests of a parallel implementation of the method for graphics processors are presented to demonstrate its effectiveness.