2016/11/30 by Ankita Mittal, Sharath S. Girimaji, Sharath Girimaji · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #A priori and a posteriori #Advanced Data Storage Technologies #Algorithm #Asynchronous communication #Asynchrony (computer programming) #Computation #Computational science #Computer science #Convection–diffusion equation #Convergence (economics) #Distributed and Parallel Computing Systems #Massively parallel #Mathematics #Parallel Computing and Optimization Techniques #Parallel computing #Scalability #Synchronization (alternating current) #physics.comp-ph
paper · pdf · doi:10.1103/physreve.96.033304
published as Phys. Rev. E 96, 033304 (2017)
arxiv created 2017/02/02 · openalex publication_date 2017/09/08 · arxiv updated 2017/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Massively parallel simulations of transport equation systems call for a paradigm change in algorithm development to achieve efficient scalability. Traditional approaches require time synchronization of processing elements (PEs), which severely restricts scalability. Relaxing synchronization requirement introduces error and slows down convergence. In this paper, we propose and develop a novel "proxy equation" concept for a general transport equation that (i) tolerates asynchrony with minimal added error, (ii) preserves convergence order and thus, (iii) expected to scale efficiently on massively parallel machines. The central idea is to modify a priori the transport equation at the PE boundaries to offset asynchrony errors. Proof-of-concept computations are performed using a one-dimensional advection (convection) diffusion equation. The results demonstrate the promise and advantages of the present strategy.