Applied Math Seminar | Jemma Shipton, Compatible finite element methods and parallel-in-time schemes for numerical weather prediction

MC 5417

Speaker

Jemma Shipton | Imperial College, London

Title

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

 Abstract

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 properties required for accuracy. However, this 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. While this sounds counterintuitive since we expect the future state of the atmosphere to depend sequentially on its past state, current research by Prof. Wingate, Dr. Shipton and others demonstrates that schemes based on exponential integrators offer the potential for large timesteps and parallel computation in evaluating the matrix exponential using a rational approximation. Of particular interest is the parareal  method, which uses an accurate timestepping scheme to iteratively refine, in parallel, the output of a computationally cheap 'coarse propagator' that can take large timesteps.