Publications

The main output of Alex's internship with the Institute for Mathematical Innovation was the publication of a research paper titled "An analytical model for wrinkle-free forming of composite laminates". In the article a novel model is developed and validated to rapidly predict the occurrence of wrinkling in the formation of composite laminate materials. Such materials find particular use in aerospace applications, and the novel model aims to act as an initial design tool to help save time and financial costs during the design stage of the manufacturing process.

In this work, we introduce and analyse discontinuous Galerkin (dG) methods for the drift–diffusion model. We explore two dG formulations: a classical interior penalty approach and a nodally bound-preserving method. Whilst the interior penalty method demonstrates well-posedness and convergence, it fails to guarantee non-negativity of the solution.

To address this deficit, which is often important to ensure in applications, we employ a positivity-preserving method based on a convex subset formulation, ensuring the non-negativity of the solution at the Lagrange nodes. 

We validate our findings by summarising extensive numerical experiments, highlighting the novelty and effectiveness of our approach in handling the complexities of charge carrier transport.