Research projects

Here is a summary of my current and past projects.

Adaptive finite element methods for mean field games

July 2024-present

I am currently a postdoctoral research fellow at University College London working within the project "Advanced numerical methods for mean field games" under the supervision of Iain Smears. Currently, we are developing adaptive finite element methods for mean field games to improve the computational efficiency and robustness compared to established methods. The first result of this project analyses the use of residual-type a posteriori error estimators for stationary second-order mean field games, and demonstrates how adaptive finite element methods performs better than conventional approaches for particular mean field games [6]. This project is in collaboration with Yohance Osborne (Durham University, UK).

Control volume finite element methods for resin transfer molding

March 2024-July 2024

As a postdoctoral research associate within the faculty of engineering at the University of Nottingham, my main responsibility was the improvement and documentation of the MATLAB software RTM-flow for fluid simulation and generating training data for resin transfer molding processes [5]. The numerical method involved a combination of finite element and finite volume methods to simulate the resin injection process from initial injection to completion. This included modelling the evolution of the moving boundary of resin liquid, and capturing the emergence of air pockets in the mold. This work was conducted under the supervision of Michael Tretyakov, Mikhail Matveev, and in collaboration with Michael Cawson and Shuang Yan.

Moving mesh virtual element methods

October 2019-June 2023

My PhD work at the University of Nottingham involved the design, analysis and implementation of moving mesh virtual element methods [1]. The main achievements of the PhD was the first successful implementation of a virtual element method for moving boundary problems [2], the analysis of isoparametric virtual element methods for high-order domain transformation [3], and the proposal of a high-order Arbitrary Lagrangian-Eulerian virtual element method for convection-diffusion problems on moving domains [4]. This PhD was supervised by Matthew Hubbard and Andrea Cangiani (SISSA, IT), and in partial collaboration with Andreas Dedner (University of Warwick, UK).