A minimal communication approach to parallel time integration

TL;DR

This paper investigates a minimal communication parallel time integration method that decomposes the time domain, computes locally, and patches solutions with minimal communication, demonstrating its efficiency and scalability through numerical experiments.

Contribution

It introduces a communication-efficient parallel time integration approach based on Nievergelt's method, with error analysis and practical scalability demonstrations.

Findings

Method reduces communication costs significantly.

Numerical simulations show good scalability on GPUs and clusters.

Competitive performance for certain problems with expensive communication.

Abstract

We explore an approach due to Nievergelt of decomposing a time-evolution equation along the time dimension and solving it in parallel with as little communication as possible between the processors. This method computes a map from initial conditions to final conditions locally on slices of the time domain, and then patches these operators together into a global solution using a single communication step. A basic error analysis is given, and some comparisons are made with other parallel in time methods. Based on the assumption that parallel computation is cheap but communication is very expensive, it is shown that this method can be competitive for some problems. We present numerical simulations on graphics chips and on traditional parallel clusters using hundreds of processors for a variety of problems to show the practicality and scalability of the proposed method.