This project will significantly contribute to advance the state-of-the-art in numerical mathematics by developing effective algorithms for scientists and engineers that use virtual design by computational modelling. The project is embedded in the EPSRC project https://gow.epsrc.ukri.org/NGBOViewGrant.aspx?GrantRef=EP/V027603/1, and it will provide unvaluable opportunities to collaborate with world-leading experts in computational mechanics both at the national and international level.
Loughborough University is a top-ten rated university in England for research intensity (REF, 2014) and an outstanding 66% of the work of Loughborough’s academic staff who were eligible to be submitted to the REF was judged as ‘world-leading’ or ‘internationally excellent’, compared to a national average figure of 43%.
In choosing Loughborough for your research, you’ll work alongside academics who are leaders in their field. You will benefit from comprehensive support and guidance from our Doctoral College, including tailored careers advice, to help you succeed in your research and future career. Find out more.
Computer simulations are an increasingly important tool to support virtual prototyping in science and engineering as they enable to reduce the time and cost of experimental testing. Virtual design aims to identify the best configuration of a system by testing several values of parameters that characterise, e.g., geometric features or material properties, and that are incorporated in the mathematical model of the system by parametrising the underlying equations. The resulting parametric problem is then solved numerically to identify the optimal configurations. This task is computationally very demanding: in practical 3D applications, numerical models can involve millions of unknowns and must be solved multiple times for each possible configuration of the system. Novel fast and reliable algorithms are thus needed to make the computational cost affordable.
This project will contribute to this very challenging research area of great practical importance for applications by developing a new computational framework that combines two mathematical methods: domain decomposition and proper generalised decomposition. These will be used to split parametric problems into collections of simpler subproblems, to solve them independently accounting for all significant values of the parameters, and to ‘glue’ the local solutions to obtain those of the original problems.
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Entry requirements for United Kingdom
Applicants should have, or expect to achieve, at least a 2:1 Honours degree (or equivalent) in Mathematics, Physics, or closely related subject. A relevant Master’s degree and/or solid experience in one or more of the following will be desirable: numerical methods for partial differential equations, computer programming (MATLAB, Python). Applicants must have an enthusiastic attitude towards innovation and commitment to develop high-quality research.
Please see the programme website for international entry requirements by country.
English language requirements
Applicants must meet the minimum English language requirements. Further details are available on the International website.
HOW TO APPLY
All applications should be made online at http://www.lboro.ac.uk/study/apply/research/. Under programme name, select Mathematical Sciences.
Please quote reference number: MD/MA/2022