A GPU Accelerated Aggregation Algebraic Multigrid Method

TL;DR

This paper introduces a GPU-accelerated aggregation algebraic multigrid method that efficiently solves large sparse linear systems from elliptic PDE discretizations, achieving grid-independent convergence with innovative aggregation and parallel algorithms.

Contribution

The paper presents a novel GPU-based aggregation algebraic multigrid preconditioner with a parallel aggregation algorithm and recursive Krylov cycles for improved efficiency and convergence.

Findings

Achieves grid-independent convergence using K-cycles.

Demonstrates superior performance over traditional methods.

Efficient GPU implementation reduces setup and solve times.

Abstract

We present an efficient, robust and fully GPU-accelerated aggregation-based algebraic multigrid preconditioning technique for the solution of large sparse linear systems. These linear systems arise from the discretization of elliptic PDEs. The method involves two stages, setup and solve. In the setup stage, hierarchical coarse grids are constructed through aggregation of the fine grid nodes. These aggregations are obtained using a set of maximal independent nodes from the fine grid nodes. We use a ``fine-grain'' parallel algorithm for finding a maximal independent set from a graph of strong negative connections. The aggregations are combined with a piece-wise constant (unsmooth) interpolation from the coarse grid solution to the fine grid solution, ensuring low setup and interpolation cost. The grid independent convergence is achieved by using recursive Krylov iterations (K-cycles) in the solve stage. An efficient combination of K-cycles and standard multigrid V-cycles is used as the preconditioner for Krylov iterative solvers such as generalized minimal residual and conjugate gradient. We compare the solver performance with other solvers based on smooth aggregation and classical algebraic multigrid methods.