I'm a PhD student in the Department of Mathematics, under the supervision of Dr. David A. Ham and Dr. Colin J. Cotter. I'm supported and funded by the EPSRC Centre for Doctoral Training in The Mathematics of Planet Earth.
My research interests are in high-performance methods for simulation science and the numerical analysis of partial differential equations. My work is inspired by the computational challenges associated with large-scale geophysical flows. In particular, I'm currently focused on developing abstractions for the automatic generation of finite element codes. Much of this work is done within the context of the Firedrake project. Some active areas I'm researching include:
- The design and analysis of compatible/mimetic finite element discretizations;
- Iterative solvers and preconditioning linear systems;
- Static condensation and hybridization techniques for finite element methods;
- High-performance and scalable code-generation software.
- Present: PhD student in Mathematics (Applied Mathematics and Mathematical Physics Section), Imperial College London, UK.
- 2018: Summer intern in Dynamics Research, Meteorological Office, Exeter, UK.
- 2016: MRes in the Mathematics of Planet Earth, Distinction, Imperial College London and University of Reading, UK.
- 2015: BSc in Mathematics, with a Secondary Major in Russian, Summa Cum Laude, Baylor University, Waco, Texas, USA.
- 2014: NSF-funded summer researcher, REU in Mathematics and Computational Science, Fairfield University, Fairfield, CT, USA.
- 2013: NSF-funded summer researcher, Center for Discrete Mathematics and Theoretical Computer Science (DIMACS), Rutgers University, New Brunswick, NJ, USA.
Shipton J, Gibson T, Cotter CJ, 2018, Higher-order compatible finite element schemes for the nonlinear rotating shallow water equations on the sphere, Journal of Computational Physics, Vol:375, ISSN:0021-9991, Pages:1121-1137
et al., Compatible Finite Element Methods for Geophysical Flows: Automation and Implementation Using Firedrake, Springer International Publishing, ISBN:9783030239565
Gibson T, 2019, thomasgibson/firedrake-springerbrief-examples: Firedrake Springerbrief Examples, v.fdspringerbrief_v0.1
Gibson T, 2019, thomasgibson/tabula-rasa: Tabula Rasa: experimentation framework for hybridization and static condensation, v.firedrake_20190329_v0
Gibson T, 2019, thomasgibson/scpc: Firedrake preconditioners for static condensation and hybridization, v.firedrake_03202019_v0