Towards parallel-in-time algorithms for numerical weather prediction

Parallel-in-time algorithms provide a route to increased parallelism for weather and climate models, addressing the issue of how to make efficient use of future supercomputers. In this talk I will present an overview of the approaches implemented in Gusto, the compatible finite element dynamical core toolkit build on top of the Firedrake finite element library. Compatible finite element methods are of interest for weather and climate modelling due to their conservation and wave propagation properties on non-orthogonal meshes such as the cubed-sphere. These non-orthogonal meshes allow for better scaling from spatial domain decomposition than meshes based on the latitude-longitude grid which have grid points clustered at the poles. However, the sequential nature of classical timestepping algorithms is a bottleneck to increased parallelisation. Numerical weather prediction is a challenging application for time-parallel schemes due to the hyperbolic nature of the partial differential equations that make up the dynamical core. Several different time-parallel schemes are under investigation in Gusto: parallel exponential integrators using a rational approximation (REXI); asymptotic parareal, which uses averaged equations to construct the coarse approximation; and schemes based on deferred correction. I will give an overview of these methods and present the latest results and challenges.