Scalability of the asynchronous discontinuous Galerkin method for compressible flow simulations

TL;DR

This paper investigates the scalability of an asynchronous discontinuous Galerkin method for compressible flow simulations, demonstrating that communication-avoiding algorithms and specialized fluxes can significantly improve parallel efficiency.

Contribution

The authors implement and analyze an asynchronous DG method with asynchrony-tolerant fluxes in deal.II, showing high-order accuracy recovery and substantial speedups in large-scale parallel simulations.

Findings

Asynchronous DG with standard fluxes degrades to first-order accuracy.

Using AT fluxes recovers high-order accuracy in asynchronous settings.

Communication-avoiding algorithm reduces synchronization overheads, achieving up to 1.9x speedup.

Abstract

The scalability of time-dependent partial differential equation (PDE) solvers based on the discontinuous Galerkin (DG) method is increasingly limited by data communication and synchronization requirements across processing elements (PEs) at extreme scales. To address these challenges, asynchronous computing approaches that relax communication and synchronization at a mathematical level have been proposed. In particular, the asynchronous discontinuous Galerkin (ADG) method with asynchrony-tolerant (AT) fluxes has recently been shown to recover high-order accuracy under relaxed communication, supported by detailed analyses of its accuracy and stability. However, the scalability of this approach in modern large-scale parallel DG solvers has not yet been systematically investigated. In this paper, we address this gap by implementing the ADG method coupled with AT fluxes in the open-source finite element library deal.II. We employ a communication-avoiding algorithm (CAA) that reduces the frequency of inter-process communication while accommodating controlled delays in ghost value exchanges. We first demonstrate that applying standard numerical fluxes in this asynchronous setting degrades the solution to first-order accuracy, irrespective of the polynomial degree. By incorporating AT fluxes that utilize data from multiple previous time levels, we successfully recover the formal high-order accuracy of the DG discretization. The accuracy of the proposed method is rigorously verified using benchmark problems for the compressible Euler equations. Furthermore, we evaluate the performance of the method through extensive strong-scaling studies for both two- and three-dimensional test cases. Our results indicate that CAA substantially suppresses synchronization overheads, yielding speedups of up to 1.9x in two dimensions and 1.6x in three dimensions compared to a baseline synchronous DG solver.