A Plug and Play Computational Framework for Efficient Virtual Prototyping in Science and Engineering (Ref: MA/MD-SF1/2026)

About the Project

Virtual prototyping is central to modern science and engineering, enabling rapid exploration of design options while reducing the cost and time associated with experimental testing. However, realistic 3D simulations often involve millions of unknowns, and must be solved repeatedly across different parameter values - making the computational burden prohibitively high.

Our PhD project will develop a new computational framework based on novel domain decomposition techniques combined with reduced order modelling, in particular proper generalized decomposition (PGD). The aim is to create a "plug and play" system that can seamlessly integrate full order models (e.g., finite elements) and efficient PGD based surrogate models. The framework will split complex parametric problems into simpler subproblems, solve them independently across parameter ranges, and then reconstruct full solutions by coupling these local contributions.

This research addresses a major practical challenge in numerical modelling and will support more efficient and reliable virtual design workflows across engineering and applied science. It contributes to real world impact by enabling faster and more affordable computational optimisation in industrial settings.

The project will be supervised by Dr Marco Discacciati, an expert in computational modelling of complex multiphysics systems, and it will benefit from collaboration with world-leading international researchers. You will join a vibrant research environment within the Department of Mathematical Sciences, benefiting from Loughborough’s strong culture of doctoral support and high quality research training.

The project will contribute to shape next-generation digital twin technologies. As such, it will help you develop advanced technical and transferable skills relevant to careers in academia, computational engineering, and high tech R&D.

Name of primary supervisor/CDT lead:
Marco Discacciati m.discacciati@lboro.ac.uk

Entry requirements:

• A Master’s degree in Mathematics, Physics, Engineering, or a closely related discipline (minimum 2:1 or equivalent).
• A solid background in numerical methods for partial differential equations.
• Strong programming skills (e.g., MATLAB, Python, C++).
• Motivation to contribute to methodological advances in computational science.

English language requirements:
Applicants must meet the minimum English language requirements. Further details are available on the International website (http://www.lboro.ac.uk/international/applicants/english/).

Bench fees required: No

Closing date of advert: 30th June 2026

Start date: October 2026

Full-time/part-time availability: Full-time 3 years

Fee band: 2025/26 Band RA (UK £5,006, International £22,360)

How to apply:
All applications should be made online. Under programme name, select Mathematical Sciences. Please quote the advertised reference number: MA/MD-SF1/2026 in your application. To avoid delays in processing your application, please ensure that you submit a CV and the minimum supporting documents. The following selection criteria will be used by academic schools to help them make a decision on your application. Please note that this criteria is used for both funded and self-funded projects. Please note, applications for this project are considered on an ongoing basis once submitted and the project may be withdrawn prior to the application deadline, if a suitable candidate is chosen for the project.

Project search terms:
applied mathematics, computational mathematics, mathematical modelling

Email Address Sci:
sci-pgr@lboro.ac.uk