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

This, within 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. de Chile. 

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

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

“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 very exceptional human quality. Undoubtedly, this collaboration has great potential which we will continue to explore in the coming years”, added the also academic from 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 computing and mathematics. Then I did a PhD in applied mathematics, where it was about numerical simulation and modeling, but not doing much analysis in the sense that I'm doing it now and most of my colleagues here do, but very much related to computing. applied to biomedicine and biomechanics”.  

Rodolfo Araya and Franz Chouly coincided years ago when carrying out their doctoral studies, as it is a center with a strong component of international exchanges. “My research topic”, explains the French researcher, “was related to applications in biomedical engineering and I had the opportunity to do a stay at the CMM”. 

After obtaining his PhD at the Grenoble INP (France), Franz agreed to a Franco-Chilean scholarship to carry out postdoctoral studies and, then, he made his first stay at the UdeC, to collaborate directly in the AN of EDPs, then under the Dr. Rodolfo Rodríguez Alonso, a UdeC academic and also a CMM associate researcher, and Dr. Gabriel Raúl Barrenechea (at that time also a UdeC academic), which lasted from October 2006 to August 2007, even before of the foundation of CI²MA (2009). 

Collaborations and new applications 

His ties with Chile continued in the family sphere, since he married a Chilean woman, and resumed his academic networks in 2020, when, while in our country for vacations, "I contacted Rodolfo (Araya) again and he told me that he was interested in developing a medical approach and had problems related to the efficiency of the model, for which we began to talk 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 are on the side of understanding phenomena that are recorded in the area of geosciences, Rodolfo Araya also being Alternate Director of the 'Precursor' Ring Project (ACT192169-ANID). 

“I had already explored Earth Sciences at the time”, Franz Chouly explains, “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 find in the field more productive than extractive, while the application that interests Rodolfo is more related to the study of earthquakes, subduction and such topics and so I began to work as an international collaborator of the Ring”. 

“What we did”, explains the French scientist, “was to go a step further towards the methods so that they can be applied to geoscience and we have a largely simplified geometry of a fault and what we want there is to write a small article aimed at geophysicists to show them that the method we have developed has interesting properties on a practical level, then it is more of 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 mechanism works very well, in general, despite the fact that we were coming out of the pandemic situation, which has delayed some administrative procedures”.  

Dr. Chouly also highlights the opportunity to carry out this stay because, since he does not have teaching tasks to fulfill, he can fully dedicate himself to research, which has had a positive impact on his scientific productivity. “Research as a full-time job, then simply not only the productivity in terms of quantity but also the quality changes. We have two articles with Rodolfo, one published in the prestigious Journal of Scientific Computing and another already sent, and we have material to write 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 gave between April and May 2022 and was aimed at students of the PhD Program in Applied Sciences with a mention in Mathematical Engineering and advanced levels of the Mathematical Civil Engineering career at the UdeC. 

New networks and projects 

In terms of collaboration networks, the French researcher highlights that this stay has also allowed them “not only to maintain our collaborations, but we began to add other people from other places to what we do, especially in applied subjects, to begin to supervise doctoral students, which would help a lot”. 

On new lines of research that could be opened from the results obtained, Franz highlights "the estimation of a posteriori error in which it is possible to adapt the mesh of a physics problem in relation to the geometry to improve the discretization quite finely for have a very precise simulation solution without a lower cost in terms of computational resources", he details in relation to an area in which UdeC specialists such as “Gabriel Gatica and Rodolfo Rodríguez, above all, have outstanding articles and are referents of his specialty”. 

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