From biomedicine to geosciences: French mathematician strengthens ties with CMM at UdeC

From biomedicine to geosciences: French mathematician strengthens ties with CMM at UdeC

Franz Chouly is on his second stay at the U. de Concepción to collaborate with the director of CI²MA and CMM associate researcher, Rodolfo Araya.


Dr. Franz Chouly, researcher and Professor at the Institut de Mathématiques de Bourgogne UMR 5584 CNRS of the Université de Bourgogne (France) will be visiting the Universidad de Concepción, UdeC, until Thursday, August 31.

This, in the framework of his collaboration with Dr. Rodolfo Araya Durán, director of the Center for Research in Mathematical Engineering (CI²MA) of the UdeC and associate researcher of the Center for Mathematical Modeling (CMM) of the U. of Chile.

The stay, which was made possible thanks to an international agreement between the CNRS and the CMM, began in September 2021 and took place in Concepción because Franz Chouly’s research interests are in the field of numerical analysis of Partial Differential Equations (PDEs NA), to which the group of mathematicians based at CI²MA is dedicated.

“Dr. Chouly’s visit has served to explore a new line of research which can be applied to different problems coming from applications, both friction and contact problems, as well as fluid mechanics problems,” Dr. Araya detailed.

“On the other hand, it has been a great experience for me since Dr. Chouly is not only a recognized specialist in his area, but also a person of exceptional human quality. Undoubtedly, this collaboration has a great potential which we will continue to explore in the coming years”, added the also academic of the Department of Mathematical Engineering of the Faculty of Physical and Mathematical Sciences of the UdeC.

Franz Chouly’s undergraduate training, he explains, was closely linked to “computer engineering and applied mathematics, and I studied computer science and mathematics. Then I did a doctorate in applied mathematics, where I dealt with numerical simulation and modeling, but without doing much analysis in the sense in which I am doing it now and most of the colleagues here do, but very much related to computation applied to biomedicine and biomechanics”.

Franz Chouly and Rodolfo Araya at CI²MA.

Rodolfo Araya and Franz Chouly met years ago during their doctoral studies at a center with a strong international exchange component. “My research topic,” explains the French researcher, “was related to biomedical engineering applications and I had the opportunity to do a stay at the CMM.”

After obtaining his PhD degree at Grenoble INP (France), Franz was awarded a French-Chilean scholarship for postdoctoral studies and then made his first stay at UdeC –to collaborate directly in NA of PDEs–, at that time under the direction of Dr. Rodolfo Rodríguez Alonso, UdeC academic and also CMM associate researcher, and Dr. Gabriel Raúl Barrenechea (then also a UdeC academic), which lasted from October 2006 to August 2007, even before the foundation of CI²MA (2009).


Collaborations and new applications

His ties with Chile continued at the family level, since he married a Chilean woman, and he resumed his academic networks in 2020, when, being in our country on vacation, “I got in touch again with Rodolfo (Araya) and he told me that he was interested in developing a medical approach and had problems related to the efficiency of the model, so we started talking and, also for personal and family reasons, I wanted to take this delegation to resume this research”.

Indeed, at present, the research interests of both scientists go around the understanding of phenomena that are observed in the area of geosciences, and Rodolfo Araya is also the Deputy Director of the Anillo ‘Precursor’ Project (ACT192169-ANID).

“I had already explored Earth Sciences at the time”, explains Franz Chouly, “collaborating in France with a semi-state company dedicated to geological and mining research, linked to fault modeling, where they contacted me to work on problems that can be found in the more productive than extractive field, while the application that Rodolfo is interested in is more related to the study of earthquakes, subduction and issues like that and so I start working as an international collaborator of the Anillo”.

“What we did”, explains the Gallic scientist, “was to take a step further towards methods so that they can be applied to geoscience and we have widely a simplified geometry of a fault and what we want there is to make a small article aimed at geophysicists to show them that the method we have developed has interesting properties at a practical level, then it is rather a natural extension of what I had done before”.

“I am very happy, the working conditions here are very good and the French-Chilean collaboration device works very well, in general, despite the fact that we were coming out of the pandemic situation, which has delayed some administrative procedures.”

Franz Chouly

Dr. Franz Chouly

Dr. Chouly, in addition, highlights the opportunity to perform this stay because, not having teaching duties to fulfill, he can devote himself entirely to research, which has had a positive impact on his scientific productivity. “Research as a full-time job, then simply not only maintains productivity in terms of quantity but also the quality changes. With Rodolfo we have two articles, one published in the prestigious Journal of Scientific Computing and another already submitted and we have material to do another two.”

Among the academic activities carried out by the French scientist during his stay, the course ‘Nitsche’s method for essential boundary conditions and some variational inequalities’ stands out, which he dictated between April and May 2022 and was directed to students of the Doctorate Program in Applied Sciences with mention in Mathematical Engineering and advanced levels of the Civil Mathematical Engineering undergraduate program of the UdeC.


New networks and projects

In terms of collaboration networks, the French researcher emphasizes that this stay has also allowed them “not only to maintain our collaborations, but also to start adding other people from other places to what we do, especially in applied topics, to start supervising doctoral students, which would help a lot”.

On new lines of research that could be opened from the results obtained, Franz highlights “the a posteriori error estimation in which it is possible to adapt the mesh of a physics problem in relation to the geometry to improve in a quite fine way the discretization to have a solution of a very precise simulation with a lower cost in terms of computational resources”, he elaborates in relation to an area in which UdeC specialists such as “Gabriel Gatica and Rodolfo Rodríguez, above all, have outstanding articles and are referents in their specialty”.

“With colleagues from Europe”, says Chouly, “we have started to put together this year an editorial project of four books with contributions from well-known people, international referents in this subject, but with an applied approach; because, in the end, there are many methods that are developed within our mathematical community of finite elements, which are being very busy in companies, by engineers, by colleagues in geosciences, biomechanics, but the community that knows the codes behind them is smaller. Among others, there will be a collaborative contribution from Rodolfo Araya and Frédéric Valentin from LNCC in Petropolis, Brazil”.

Posted on Aug 28, 2023 in News