Computational Methods for Evolving-Domain Problems with Application to Phase Transitions in Materials

This interdisciplinary PhD project at the University of Greenwich offers an exciting opportunity to advance computational methods for evolving-domain problems, with a particular focus on phase transitions in materials. The research unites applied mathematics, computational mathematics, and engineering, targeting the development and improvement of numerical approaches for partial differential equations (PDEs) defined on domains with time-dependent interfaces, known as free-boundary problems. Physical phenomena such as the formation of oxides or solid-electrolyte interphases in battery electrodes involve propagating interfaces between distinct material phases. These interfaces are often described by highly non-linear PDEs, and their computational handling remains a significant challenge. The project aims to further develop the cut-finite-element method, which treats phase boundaries as sharp interfaces moving across a fixed finite-element mesh. The focus will be on enhancing the accuracy and efficiency of this computational approach for a range of material systems exhibiting multi-physics behaviour, including chemo-mechanical and magneto-mechanical systems. The successful candidate will join the Computational Science and Engineering Group (CSEG) within the Faculty of Engineering and Science, becoming part of a dynamic and growing research team with extensive expertise in computational materials modelling and phase transformation processes. The project is supervised by Dr Mikhail Poluektov, Prof Andrew Kao, and Dr Ivars Krastins, ensuring strong academic guidance and support. This studentship is fully funded by the M34Impact programme, a £9 million Expanding Excellence in England (E3) grant. The funding package includes a generous stipend, London weighting, enhanced bursary, and a contribution to tuition fees at the University Home Rate. International applicants may need to cover the remainder of tuition fees unless exceptionally supported by the programme. The bursary is for three years, with the possibility of a 12-month extension if progress is satisfactory. Applicants should have a strong academic background in applied mathematics, computational mathematics, or engineering, with experience in numerical methods for PDEs and materials modelling. A first or upper second class degree (or equivalent) in a relevant subject is required. International candidates must meet English language requirements and may be responsible for additional tuition fees. The application deadline is March 31, 2026. Interested candidates should apply online via the University of Greenwich portal, submitting a CV, academic transcripts, and a cover letter. For further details, refer to the FindAPhD project link provided.