A scalable weakly-synchronous algorithm for solving partial differential equations

TL;DR

This paper introduces a weakly-synchronous algorithm using novel asynchrony-tolerant schemes for PDEs, significantly reducing synchronization overheads and improving scalability on large supercomputers, paving the way for exascale computing.

Contribution

It presents a new weakly-synchronous algorithm with asynchrony-tolerant finite-difference schemes and demonstrates its scalability and efficiency on large-scale systems.

Findings

Speedup of up to 3.3x in communication time

Total runtime reduction of 2.19x

Effective scalability demonstrated on supercomputers

Abstract

Synchronization overheads pose a major challenge as applications advance towards extreme scales. In current large-scale algorithms, synchronization as well as data communication delay the parallel computations at each time step in a time-dependent partial differential equation (PDE) solver. This creates a new scaling wall when moving towards exascale. We present a weakly-synchronous algorithm based on novel asynchrony-tolerant (AT) finite-difference schemes that relax synchronization at a mathematical level. We utilize remote memory access programming schemes that have been shown to provide significant speedup on modern supercomputers, to efficiently implement communications suitable for AT schemes, and compare to two-sided communications that are state-of-practice. We present results from simulations of Burgers' equation as a model of multi-scale strongly non-linear dynamical systems. Our algorithm demonstrate excellent scalability of the new AT schemes for large-scale computing, with a speedup of up to $3.3$x in communication time and $2.19$x in total runtime. We expect that such schemes can form the basis for exascale PDE algorithms.