Compatible finite element methods and parallel-in-time schemes for numerical weather prediction.

I will describe Gusto, a dynamical core toolkit built on top of the Fire- drake finite element library; present recent results from a range of test cases and outline our plans for future code development.

Gusto uses compatible finite element methods, a form of mixed finite element methods (meaning that different finite element spaces are used for different fields) that allow the exact representation of the standard vector calculus identities div-curl=0 and curl-grad=0. The popularity of these methods for numerical weather prediction is due to the flexibility to run on non-orthogonal grid, thus avoiding the communication bottleneck at the poles, while retaining the necessary convergence and wave propagation prop- erties required for accuracy.

Although the flexibility of the compatible finite element spatial discreti- sation improves the parallel scalability of the model it does not solve the parallel scalability problem inherent in spatial domain decomposition: we need to find a way to perform parallel calculations in the time domain. Ex- ponential integrators, approximated by a near optimal rational expansion, offer a way to take large timesteps and form the basis for parallel timestep- ping schemes based on wave averaging. I will describe the progress we have made towards implementing these schemes in Gusto.