Maths, business & society: portrait of Alice Nassor

Sponsored by the learned societies Société Française de Statistique (SFDS), the Société de Mathématiques Appliquées et Industrielles (SMAI) and the Société Mathématique de France (SMF), the 2024 thesis prize was awarded at the 13th edition of the Forum Entreprises & Mathématiques on Monday, October 7, 2024.

• Title of thesis: Domain decomposition method for coupled acoustic-elastic problems in the time domain. Application to underwater explosions.
• University of issue: Institut Polytechnique de Paris
• Thesis supervisors: Stéphanie Chaillat and Marc Bonnet (Laboratoire Poems1 )
• Industrial supervisors: Bruno Leblé (Naval Group)
• Company: Naval Group
• Industrial partner: Direction Générale de l'armement (DGA)
• Currently research engineer in the mechanics department of the Institut français du pétrole et énergies nouvelles (IFPEN)

How did your collaboration with Naval Group begin?

After studying mechanical engineering, I focused on numerical methods in my master's degree (coupled calculation, structural calculation, modeling, etc.). I really wanted to pursue more mathematical studies, so I was looking for a thesis in math. I was also interested in the links with structures, subjects related to maritime engineering, to naval engineering. I found a thesis subject that corresponded to everything I was looking for, both in terms of industrial applications and “technical” research. My thesis supervisors had already successfully set up a thesis collaboration between my laboratory and Naval Group. The collaboration therefore continued with a second thesis subject, and that's when it happened: I was in my second year of a Master's degree and the subject corresponded perfectly with what I wanted to do. It was a great opportunity! My thesis was also carried out in collaboration with the Direction Générale de l'Armement (DGA), which joined the collaboration with Naval Group at a later date.

Can you tell us about your thesis topic?

The objective was to develop numerical methods and, at the same time, to model quickly and accurately the interaction with a structure that occurs when a submarine is subjected to a distant underwater explosion. Industrial software has been available for a very long time for this purpose, but it is old and based on approximations of equations. The idea is therefore to develop a new modeling tool to solve this problem. To do this, finite elements are used to model the behavior of the underwater structure, and a method called “boundary elements”, based on integral boundary equations, to model the ocean, which is an infinite environment. The challenge of the thesis was to try to combine these two methods. These problems have a very fast dynamic, so we needed an effective method. But the first numerical tests did not converge. So we turned to domain decomposition theories to try to better understand the mathematical problems at stake and develop a convergent strategy to combine our two numerical methods.

What were the main challenges you encountered during your research?

As my thesis subject was industrial, we had to rely on a particular commercial finite element solver, i.e. the one used by Naval Group engineers. However, this particular solver does not allow us to use a certain type of boundary condition that we needed to use for our coupling to work. In consultation with Naval Group, we then selected another finite element solver. This one is open source. This was important because we are developing a tool, of course, but we want it to be usable by engineers afterwards, so it has to meet their needs. The discussions were interesting: in the development of the coupling, of the very upstream research, we were already taking into account the digital tools that were going to be used later. I found it very interesting to guide research in relation to engineering needs.

What practical applications of your research do you see emerging in the future?

This thesis will provide a better understanding of elastic acoustic problems. We have shown in which functional framework these problems can be solved, what types of boundary conditions can be used, etc. It's still really maths, but we have nevertheless advanced the understanding of mechanical problems, which can be used in many fields. This work can be used in fields other than naval engineering, even if the code that came out of the thesis currently belongs to Naval Group.

What advice would you give to young people who want to focus their research in mathematics on concrete applications?

I would advise them to choose their courses carefully and to take an interest in scientific content before application. The latter is certainly very important, but when you do research it is important to love scientific content. Even one type of science can have many different applications. Obviously, choosing the right laboratory and thesis supervisors well is important, perhaps even more so than choosing the thesis subject, because that's what makes a project well-run and rewarding. A thesis is still a collective work, so the choice of team is central. For my part, I was supervised by five people, all with their own point of view. It was very enriching!

How do you see the role of mathematics in solving current societal problems?

In my thesis subject, it is really thanks to mathematics that we have succeeded in understanding how simulations and software work. Going back to fundamental mathematics has enabled us to understand numerical tools and improve them. We need maths, not just to use the codes but to understand what is behind them.

As a young researcher, how do you perceive the changing relationship between academic research in mathematics and the socio-economic world?

In the laboratory where I was, there is a lot of collaboration with companies. When you want to do applied mathematics, I think it's great to be able to work on concrete and realistic subjects. Overall, I get the impression that the partners, whether academic or industrial, want to collaborate.

• 1CNRS/Inria/ENSTA