Research Fellow

About the role

We are seeking a highly motivated and talented applicant to join the research group of Dr Iain Smears (Principal Investigator) on the EPSRC project Advanced Numerical Methods for Mean Field Games, Grant EP/Y008758/1. The focus of this project is on adaptive numerical methods for Mean Field Games (MFG), which originate in models of stochastic control and stochastic games. MFG models are relevant to applications of societal importance, such as in energy, financial stability and the environment, which connect to several of the strategic priority areas highlighted by EPSRC. The overall aim of the project is to develop state-of-the-art adaptive finite element methods for Mean Field Games. This includes the development of novel mathematical theory for the rigorous analysis of the numerical methods, the design of novel algorithms to handle the challenging structures of the MFG system, and the implementation of the methods in scientific software codes. The Numerical Analysis Group at UCL consists of five permanent faculty members, including Dr Iain Smears (PI), Dr M. Jensen, and Profs E. Burman, T. Betcke and D. Hewett. The group has expertise across the range of computational mathematics, with special strengths of the group are in the analysis of finite element methods, the numerical analysis of nonlinear partial differential equations, and the numerical simulation of wave phenomena. The group also comprises PhD students and postdoctoral researchers. We organize a bi-weekly Numerical Analysis seminar shared with Imperial College London, and regularly host national and international speakers. The group also regularly organises scientific workshops at UCL, such as the recent workshop on Numerical Methods for Mean Field Games and Related PDE, and the upcoming European Finite Element Fair in 2024. The post is available from 1st July 2024 or as soon as possible thereafter, and is funded for approximately 36 months until 30th June 2027 at the latest in the first instance , due to funding restrictions. Duties and responsibilities Research The successful candidate will carry out high-level research at the forefront of the field on numerical methods for the partial differential equations as part of the EPSRC research grant Advanced Numerical Methods for Mean Field Games. The successful candidate will conduct research on all aspects of the numerical analysis of the problems, including developing new mathematical theory of the numerical methods, implementing the algorithms in finite element software libraries and performing extensive numerical computations. The successful candidate will regularly submit research findings for publications in refereed journals. The successful candidate will also present research findings at regular national and international conferences, interface with other team members, and participate in seminars and research activities of the group. Teaching The successful candidate will teach one undergraduate level course per year, i ncluding writing and marking of examinations and carry out the duties of 2nd examiner. Management and Administration The successful candidate will assist in the organization of a scientific events, such as workshops and conference minisymposia, and all other required administrative tasks required by the research project.

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