Tempered Finite Elements

This Ph.D. is being carried out as part of the X-MESH project, an ERC/SYNERGY project led by Professors Jean-François Remacle and Nicolas Moes, both of whom are professors at the Université Catholique de Louvain in Belgium.

The X-MESH project aims to develop an original method for numerically calculating solutions to partial differential equations with discontinuous coefficients: in this case, fronts can appear, move, coalesce or disappear, and calculating the geometry of these fronts is complex. The X-MESH approach consists of considering that the geometry of the problem is part of the solution to be calculated.

More specifically, this Ph.D. peroject deals with one of the first outcomes of our project, the Tempered Finite Element Method. The Tempered Finite Element Method (TFEM) extends the Finite Element Method (FEM) to classes of meshes that include zero-measure or nearly degenerate elements for which standard FEM approaches do not allow convergence.

With TFEM, it is possible to calculate complex fluid-structure interaction problems without changing the mesh, even when two structures come into contact. The idea is, as we have shown, to degenerate meshes when two solids are in contact and continuously transform a 3D problem into a 2D problem (frictional contact). In this thesis, we plan to apply TFEMs to aquaplaning, in collaboration with a major company in the field.

The Universite catholique de Louvain (https://uclouvain.be/fr/index.html) is a comprehensive university with over 40,000 students.

The UCLouvain campus is located less than 30 km from Brussels, the capital of Europe. Louvain-la-Neuve is a new, car-free town with a large number of reasonably priced homes, a very active cultural life and high-quality schools for children.

Our team -- X-MESH -- comprises around 10 PhD students, 5 post-docs and 4 permanent staff, split between UCLouvain (the project's 2 PI's are at UCLouvain) and the Ecole Centrale de Nantes. The Ph.D. is located at UCLouvains on the Louvain-la-Neuve site.

A thesis in Belgium, at UCLouvain, takes 4 years to complete. The salary for a PhD student is competitive with those offered in industry (2500€+ all taxes paid), with attractive benefits such as 2 days per week teleworking and reimbursement of UCLouvain-to-home journeys by public transport.

We are looking for a candidate who is motivated by the theoretical and computational aspects of numerical mechanics. The ideal candidate will have a master's degree in engineering sciences, specialising in mechanics or applied mathematics, or equivelently a master's degree in math/meca.

A good knowledge of English is required. The working language at UCLouvain is French, but the working environment is 100% English Speakign Friendly.