Using performance analysis tools for parallel-in-time integrators -- Does my time-parallel code do what I think it does?

TL;DR

This paper demonstrates how performance analysis tools can be applied to the PFASST parallel-in-time integrator within pySDC, revealing insights and potential pitfalls to improve correctness and efficiency.

Contribution

It provides a practical example of applying performance analysis tools to a complex parallel-in-time code, offering a blueprint for similar future analyses.

Findings

Identified obstacles in the implementation of PFASST

Described remedies for common pitfalls

Uncovered surprising insights through analysis

Abstract

While many ideas and proofs of concept for parallel-in-time integration methods exists, the number of large-scale, accessible time-parallel codes is rather small. This is often due to the apparent or subtle complexity of the algorithms and the many pitfalls awaiting developers of parallel numerical software. One example of such a time-parallel code is pySDC, which implements, among others, the parallel full approximation scheme in space and time (PFASST). Inspired by nonlinear multigrid ideas, PFASST allows to integrate multiple time-steps simultaneously using a space-time hierarchy of spectral deferred corrections. In this paper we demonstrate the application of performance analysis tools to the PFASST implementation pySDC. Tracing the path we took for this work, we highlight the obstacles encountered, describe remedies and explain the sometimes surprising findings made possible by the tools. Although focusing only on a single implementation of a particular parallel-in-time integrator, we hope that our results and in particular the way we obtained them are a blueprint for other time-parallel codes.