Project: Scalable Iterative Methods for Compatible Finite Element Ocean Modelling
Supervisors: Prof. Colin Cotter joint with Dr. Josh Hope-Collins
Project Description:
High fidelity computer models of the ocean play a crucial role in understanding climate change and forecasting weather and extreme events. It is important to improve and build more reliable models compared to current prediction tools. Over the last decade there has been a drive to build new ocean models with unstructured meshes that can allow focus on a particular region for regional climate or process studies, and to more precisely represent coastlines and topography where these details strongly impact global circulation. Further, new algorithms need to be developed to make use of the next generation of supercomputers whose architectural designs are heavily guided by the requirements of modern AI.
In my proposed research, I will focus on developing an approachable unstructured mesh model for global ocean dynamics that reaches high accuracy, stability and performance on massively parallel supercomputers. Building on the adoption of compatible finite element methods by the Met Office for their next generation climate and weather model, I will enter a design cycle for a compatible finite element ocean model, implemented using an (Imperial-led) automated finite element software package, Firedrake . Compatible finite elements, the subject of my proposed research, address the problem of spurious numerical waves that cause large unphysical numerical errors . A rigorous stability analysis of the mathematical algorithm considering the inner computational core will be conducted, using the fundamental theory of the finite element exterior calculus (FEEC).
Firedrake will be used to implement the solver in practice, leveraging its capability for moving rapidly from prototypes running on laptops up to massively parallel supercomputers. A foundational ocean dynamical core will be developed and benchmarked the following steps:
1. Construct an efficient and scalable solver for the linear Boussinesq system with free surface in thin domains.
2. Incorporate capability for active tracers such as salinity.
3. Design an efficient splitting method for time stepping.
4. Benchmark our model on idealised 3D problems in the literature used in the development pathway.
This will be accompanied in parallel by analysis of the algorithm stability giving rigorous guidance on the suitability of my new solver within the design cycle.
