A novel and scalable Multigrid algorithm for many-core architectures

TL;DR

This paper introduces a scalable multigrid algorithm optimized for many-core architectures like GPUs, achieving high efficiency by fusing operations and avoiding CPU-GPU data transfers, with linear scaling and perfect scalability.

Contribution

The paper presents a novel high occupancy multigrid (HOMG) algorithm that operates entirely within GPU memory, enhancing parallelism and scalability for large linear systems.

Findings

Linear scaling of operations with grid size

Perfect scalability across many processors

Efficient GPU-only multigrid implementation

Abstract

Multigrid algorithms are among the fastest iterative methods known today for solving large linear and some non-linear systems of equations. Greatly optimized for serial operation, they still have a great potential for parallelism not fully realized. In this work, we present a novel multigrid algorithm designed to work entirely inside many-core architectures like the graphics processing units (GPUs), without memory transfers between the GPU and the central processing unit (CPU), avoiding low bandwitdth communications. The algorithm is denoted as the high occupancy multigrid (HOMG) because it makes use of entire grid operations with interpolations and relaxations fused into one task, providing useful work for every thread in the grid. For a given accuracy, its number of operations scale linearly with the total number of nodes in the grid. Perfect scalability is observed for a large number of processors.