Extending DD-$\alpha$AMG on heterogeneous machines

TL;DR

This paper extends the DD-αAMG multigrid solver for lattice QCD to heterogeneous architectures by porting to HIP, adding new smoothers, and optimizing coarse-grid operations for improved performance on supercomputers.

Contribution

It introduces a HIP-based port of DD-αAMG, extends available smoothers with Richardson smoothing, and enhances coarse-grid operations with advanced vectorization.

Findings

Richardson smoothing outperforms GCR smoothing in speed.

HIP port enables running on ORISE supercomputer.

Enhanced coarse-grid operations improve computational efficiency.

Abstract

Multigrid solvers are the standard in modern scientific computing simulations. Domain Decomposition Aggregation-Based Algebraic Multigrid, also known as the DD-$\alpha$AMG solver, is a successful realization of an algebraic multigrid solver for lattice quantum chromodynamics. Its CPU implementation has made it possible to construct, for some particular discretizations, simulations otherwise computationally unfeasible, and furthermore it has motivated the development and improvement of other algebraic multigrid solvers in the area. From an existing version of DD-$\alpha$AMG already partially ported via CUDA to run some finest-level operations of the multigrid solver on Nvidia GPUs, we translate the CUDA code here by using HIP to run on the ORISE supercomputer. We moreover extend the smoothers available in DD-$\alpha$AMG, paying particular attention to Richardson smoothing, which in our numerical experiments has led to a multigrid solver faster than smoothing with GCR and only 10% slower compared to SAP smoothing. Then we port the odd-even-preconditioned versions of GMRES and Richardson via CUDA. Finally, we extend some computationally intensive coarse-grid operations via advanced vectorization.