A Parallel Auxiliary Grid AMG Method for GPU

TL;DR

This paper introduces a GPU-optimized parallel auxiliary grid AMG method that leverages a fixed coarsening procedure and specialized smoothing to achieve significant speedups in solving large linear systems.

Contribution

A novel parallel auxiliary grid AMG algorithm designed for GPUs, featuring explicit control of sparsity, load balancing, and a specialized coloring smoother for improved performance.

Findings

Achieves over 4x speedup on quasi-uniform grids

Achieves over 2x speedup on shape regular grids

Demonstrates efficiency and scalability of the GPU implementation

Abstract

In this paper, we develop a new parallel auxiliary grid algebraic multigrid (AMG) method to leverage the power of graphic processing units (GPUs). In the construction of the hierarchical coarse grid, we use a simple and fixed coarsening procedure based on a region quadtree generated from an auxiliary grid. This allows us to explicitly control the sparsity patterns and operator complexities of the AMG solver. This feature provides (nearly) optimal load balancing and predictable communication patterns, which makes our new algorithm suitable for parallel computing, especially on GPU. We also design a parallel smoother based on the special coloring of the quadtree to accelerate the convergence rate and improve the parallel performance of this solver. Based on the CUDA toolkit [40], we implemented our new parallel auxiliary grid AMG method on GPU and the numerical results of this implementation demonstrate the efficiency of our new method. The results achieve an average speedup of over 4 on quasi-uniform grids and 2 on shape regular grids when compared to the AMG implementation in CUSP.