A micro/macro parallel-in-time (parareal) algorithm applied to a climate model with discontinuous non-monotone coefficients and oscillatory forcing

TL;DR

This paper applies a micro/macro parareal algorithm to a complex 1-D climate model with challenging coefficients and forcing, demonstrating faster convergence and significant computational gains through parallel processing.

Contribution

It introduces a novel micro/macro parareal approach tailored for a 1-D climate model with discontinuous and oscillatory features, showing improved convergence and efficiency.

Findings

The method converges in fewer iterations than the number of subintervals.

A theoretical performance gain of up to 10 times is achievable.

Different macro models and micro schemes affect convergence and efficiency.

Abstract

We present the application of a micro/macro parareal algorithm for a 1-D energy balance climate model with discontinuous and non-monotone coefficients and forcing terms. The micro/macro parareal method uses a coarse propagator, based on a (macroscopic) 0-D approximation of the underlying (microscopic) 1-D model. We compare the performance of the method using different versions of the macro model, as well as different numerical schemes for the micro propagator, namely an explicit Euler method with constant stepsize and an adaptive library routine. We study convergence of the method and the theoretical gain in computational time in a realization on parallel processors. We show that, in this example and for all settings, the micro/macro parareal method converges in fewer iterations than the number of used parareal subintervals, and that a theoretical gain in performance of up to 10 is possible.