Contributed Talk
Towards parallel-in-time methods for the moist shallow water equations
University of Exeter, UK
Abstract
Weather and climate forecasting rely heavily on the use of supercomputers to numerically solve the PDEs that describe the evolution of the atmosphere. The changing trend in supercomputer architecture towards massively parallel systems is motivating a redesign of forecasting algorithms to support routes to parallelism. In particular, we are interested in the problem of parallel temporal discretisation of the equations, and are investigating several routes to time parallelism for these PDEs. These include schemes based on exponential integrators, parallelised through the use of a rational approximation which approximates the integral as a sum (the terms of which can be computed in parallel), as well as schemes based on predictor-corrector methods such as integral deferred correction and parareal. A natural starting point in the design of these algorithms is the rotating shallow water equations, which are the usual test bed for atmospheric model development. As a simpler model than the full three-dimensional system the shallow water equations are computationally cheap, but they retain the challenge of timescale separation present in the full equations due to the presence of both slow Rossby waves and faster inertial-gravity waves. The addition of moisture to the system introduces an additional challenge due to the switch-like forcing. I will present an overview of our approach to investigating time-parallel methods for these equations using the Gusto finite element dynamical core toolkit, and show results from recent test cases.