The Finite Element Method (FEM) is widely used for numerical simulation in Engineering, for example in modelling deformable solids. While significant advances have been made in many aspects of the method, most FEM implementations rely on standard polynomial interpolations and Gaussian numerical integration. Recent results in numerical integration for higher order polynomial FEM interpolations show that significant improvements in computational efficiency can be obtained by developing customised formulations. The effort involved in developing such customised formulations, however, currently limits the applicability of this approach. This PhD project will focus on developing an automated framework for developing, testing, and selecting non-standard interpolation and integration methods leading to highly efficient FEM formulations, adapted to the characteristics of the input problem. Established heuristic optimisation approaches will be complemented by novel AI/agentic techniques to locate optimal formulations across a wide search space. The research in this project will be based on existing preliminary work and proof-of-concept tools using both computer algebra software for symbolic calculations (Maple) and numerical computation software (Matlab, Python or Julia). Specific new results obtained through the automated framework will be implemented and tested within commercial computational mechanics codes, such as the Abaqus FEM software. Closing date: 31 May, 2026 Apply now Principal Supervisor Dr Stefanos Aldo Papanicolopulos Assistant Supervisor Dr Nicholas Polydorides Eligibility Minimum entry qualification - an Honours degree at 2:1 or above (or International equivalent) in a relevant science or engineering discipline, possibly supported by an MSc Degree. Applicants must demonstrate an appropriate background in numerical analysis, programming, mechanics of materials and/or computational mathematics.Further information on English language requirements for EU/Overseas applicants. Funding Applications are welcomed from self-funded students, or students who are applying for scholarships from the University of Edinburgh or elsewhere as well as self-funded students.Competition (EPSRC) funding may be available for an exceptional candidate. Link below for the further details.Further information and other funding options.
