Local time stepping for the shallow water equations in MPAS

TL;DR

This paper evaluates local time-stepping schemes for the shallow water equations in MPAS, focusing on their efficient parallel implementation to enhance simulation speed and scalability in climate modeling.

Contribution

It presents a scalable parallel implementation of LTS methods for MPAS, addressing load balancing and computational challenges to improve performance.

Findings

LTS schemes can significantly accelerate shallow water simulations.

Proper parallelization is crucial for maintaining scalability.

The implementation achieves efficient load balancing and computational performance.

Abstract

We assess the performance of a set of local time-stepping (LTS) schemes for the shallow water equations implemented in the Model for Prediction Across Scales (MPAS). The goal of LTS is to speed up the simulation by allowing different time-steps on different regions of the computational grid. The LTS schemes considered here were originally introduced by Hoang et al. (J. Comput. Phys., Vol. 382, p.152-176, 2019), who laid out the mathematical foundation of the methods. Here, the authors take on the task of presenting a fast, efficient and scalable parallel implementation of these LTS methods on high performance computing machines, with the aim to provide a recipe for other climate modeling groups that may be interested in employing LTS algorithms in their codes. As a matter of fact, even if MPAS is our framework of choice, our approach is general enough and could be of interest to other groups beyond the MPAS community. Due to their nature, LTS methods possess an inherent load imbalance that needs to be carefully addressed in order to obtain efficient scalability. Even more important is the far from trivial task of computing the right-hand side terms only on specific LTS regions during the time-stepping procedure. An inefficient handling of this task causes a drastic decay of the CPU time performance, making the LTS algorithms practically of no use. The emphasis of the present work is therefore on the computational and parallel aspects of the LTS methods, whose proper handling is crucial to make the methods run faster against existing strategies, such as for instance high-order explicit global time-stepping schemes. This is in fact the ultimate goal of using an LTS procedure and it is the one to which we direct all our optimization efforts.