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.

[£22,780 to £24,780 per annum bursary for 3 years (potential extension up to 12 months); contribution to tuition fees at University Home Rate (£5,006/year); international applicants may need to pay remainder tuition fee unless covered by M 3 4Impact.] This interdisciplinary PhD studentship 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 project bridges 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 and solid-electrolyte interphases in battery electrodes involve propagating interfaces between distinct material phases. These interfaces are modeled as sharp boundaries moving across fixed finite-element meshes, presenting significant computational challenges, especially in highly non-linear cases. The project aims to further develop the cut-finite-element method to enhance accuracy and efficiency in simulating phase transitions in materials, including multi-physics systems like chemo-mechanical and magneto-mechanical processes. The successful candidate will join the Computational Science and Engineering Group (CSEG), a dynamic research team with expertise in computational materials modelling and phase transformation processes. The studentship is fully funded by the M 3 4Impact programme, part of a £9 million Expanding Excellence in England (E3) grant, providing access to training and research initiatives. Supervision will be provided by Dr Mikhail Poluektov, Prof Andrew Kao, and Dr Ivars Krastins, ensuring strong academic guidance and support. Funding includes a bursary of £22,780 to £24,780 per annum for three years, with a possible extension of up to 12 months. Tuition fees are covered at the University Home Rate (£5,006/year), and exceptional international applicants may have their full tuition fees covered. International applicants should note that they may need to pay the remainder tuition fee unless covered by the funding programme. Applicants should possess a strong academic background in applied mathematics, computational mathematics, or engineering, with experience in numerical methods for PDEs and mechanics of materials. A first-class or upper second-class undergraduate degree (or equivalent) in mathematics, physics, engineering, or a related discipline is preferred. Experience with finite element methods, computational modelling, or phase transitions in materials is advantageous. English language requirements may apply for international candidates. To apply, submit your application online via the University of Greenwich portal, including your CV, academic transcripts, and a cover letter outlining your suitability for the project. The application deadline is 17 April 2026. For further information, contact the supervisors or visit the project link provided.