2 semesters at KTH for Thomas

Academically, this double degree at KTH has enabled me to consolidate and broaden my skills in CFD, optimization and the simulation of complex systems more generally. These are skills that I consider to be very interesting for the engineering career I want to pursue in the future. I was also able to greatly improve my language skills, as all courses were taught in English. I also appreciated the excellent quality of teaching at KTH: the courses were generally efficient, concise and at the same time very clear. Numerous group projects were integrated into the teaching, encouraging both the practical application of theoretical knowledge and the development of interpersonal skills.

During the first half of my first semester at KTH, I took several compulsory courses for students in the applied mathematics program:

• The first, focusing on probability theory, aimed to harmonize the students’ level by going back to the fundamentals. Although most of the concepts covered had already been dealt with during my preparatory class and my first two years at ISAE-SUPAERO, this course was still useful, as it covered new concepts that other international students had already tackled.

• A second course focused on the challenges of sustainable development (SDGs), climate impact and gender inequality, particularly in the fields of research and science.
• A final compulsory course was designed to train us in philosophical issues related to research and engineering. We discussed methodology, ethics, design and risk management. It was a very interesting course, as I’ve never dealt with these issues before in my studies.

The rest of the courses I took were of my own choosing. In the first semester, I mainly chose courses providing a grounding in data processing and numerical simulation. I first had a course on the methods used to solve ordinary and partial differential equations numerically. The emphasis was on analyzing the stability and accuracy of the methods studied. This course was very useful for simulating simple models and was a first introduction to the CFD courses I had later in the year. In the second half of the first semester, I took a course entitled “Matrix computations for large-scale systems”. It provided various numerical techniques used to solve problems with high-dimensional matrices (eigenvalue determination, system inversion, QR decomposition, matrix functions, etc.). These methods find concrete applications not only in data processing, but also in many scientific fields, where solving linear systems is an essential step. I’ve also been able to reuse these tools in my optimization and CFD courses. Although these techniques are often integrated into software libraries, understanding their theoretical underpinnings remains crucial to using them effectively and appropriately.

For the second semester, I took courses with more concrete applications. First of all, I took a linear optimization course, deepening the concepts I’d already covered in Toulouse. In addition to reviewing integer linear programming (ILP), I discovered new concepts such as stochastic programming and advanced decomposition techniques, notably the Danzig-Wolfe method. This course was very enriching thanks to the quality of the teaching provided by Jan Kronqvist, a researcher specialized in MIP with recognized experience in industrial optimization applications. At the same time, I was taking a CFD course. After a review of the fundamentals of fluid mechanics and numerical methods for solving differential equations, the course provided an overview of the classical approaches used to simulate fluid systems. In particular, we studied the finite volume method, the different approximations of the Navier-Stokes equations that can be used, the different meshing strategies, the use of multigrids, and so on. The course concluded with the realization of a simplified solver for incompressible Navier-Stokes equations, implemented on Matlab.

Finally, my last semester ended with a course in non-linear optimization and an advanced CFD course, extending the notions covered previously. The non-linear optimization course allowed me to go further than what I had studied in France, notably with the study of Sequential Quadratic Programming and Semidefinite Programming, used in complex optimization contexts. The advanced CFD course focused on the application of the adaptive finite element method to the solution of Navier-Stokes equations, mainly through the use of the Python FEniCS library. Topics covered included numerical stabilization, dynamic mesh adaptation, and modeling of boundary layer, shock and turbulence phenomena. Although this course was rather research-oriented, it was nevertheless a good introduction to understanding the critical parameters involved in modern CFD software, beyond the classical finite volume method. The course concluded with a research project of the students’ choice. For my part, I chose to study the potential energy savings obtained by flying in V-formation, a subject combining numerical modeling and aerodynamic optimization.

What has made a lasting impression on you culturally?

From a cultural point of view, this experience gave me an in-depth insight into Swedish traditions. When I arrived in Sweden, I was warmly welcomed by the THS international reception, the KTH students’ association. I had the opportunity to visit several of Stockholm’s iconic sites, such as Gamla Stan (the Old Town), the Royal Palace, Stockholm City Hall (Stadshuset) and the Bay, all as part of affordable student activities. I had my first fika, traditional coffee breaks accompanied by kanelbullar (cinnamon buns). I had my first gasques and sittningar, festive three-course dinners punctuated by traditional student songs. I was particularly impressed by KTH’s main campus, with its red-brick architecture reminiscent of the industrial era. This immersion also enabled me to practice my English on a daily basis, as the vast majority of Swedes have a perfect command of the language. Finally, I was struck by Stockholm’s remarkable cleanliness, efficient organization and exceptional quality of life.

During my year, I also had the opportunity to discover the city’s cultural wealth through visits to several emblematic museums. These included the Vasa Museum, home to an exceptionally well-preserved 17th-century shipwreck, and Skansen, an open-air museum showcasing Swedish folk culture and traditional crafts. The latter also includes a zoological park showcasing the diversity of Nordic fauna. I also explored several museums dedicated to Swedish history, and more specifically to the Viking era, which plays an important role in the country’s cultural identity. At the same time, I had the chance to attend various musical events, including the Stockholm Jazz Festival and the Nuit de la Culture, which offer many free concerts accessible to all. More generally, my life in Stockholm was punctuated by the great traditional Swedish celebrations such as Saint Lucia’s Day and Walpurgis Night.

Beyond national traditions, I also discovered the richness of Swedish student culture. Already at KTH, I had experienced the principle of chapters, associations bringing together all students from the same program (the physics chapter in my case). Each chapter has its own premises and regular activities are organized for chapter members. There are also numerous clubs at KTH, both sporting and artistic. Among them, the KTH Outdoor Club organizes nature outings such as hiking, trail running and kayaking, allowing you to discover the beauty of the Swedish countryside. However, my main source of fulfillment has been the Studentorkester culture, student orchestras often oriented towards jazz or pop that can be found mainly in Sweden and Norway, but also in Finland and Germany. I joined Kårsdraget, the University of Stockholm’s orchestra, which also enabled me to progress my instrumental playing, which I had started with the ISAE-SUPAERO brass band. We were able to give a concert in November and took part in festivals (BRUNK in Uppsala and SOF in Linköping, for example), enabling us to meet other orchestras, both Swedish and foreign. It was also in this context that I discovered the widespread use of patches in Sweden: embroidered badges that students affix to their clothing to commemorate significant events, concerts, festivals, or simply to express their humor and creativity.

Finally, I was also lucky enough to be able to travel to several regions of Scandinavia. In particular, I explored the Stockholm archipelago through hiking, discovered the island of Gotland and its medieval town of Visby, and visited Nordic capitals such as Copenhagen in Denmark and Turku in Finland. But the most memorable experience of my stay was undoubtedly my trip to Swedish Lapland and Norway’s Lofoten Islands. In Kiruna, I experienced extreme climatic conditions, with temperatures hovering around -30°C. I was lucky enough to observe the Northern Lights from the famous Arctic train. Finally, I was deeply impressed by the spectacular landscapes and natural diversity of the Lofoten Islands. It will remain a visual and emotional memory that I’ll probably treasure for the rest of my life.

If you had to make a more personal assessment of your stay, what would you retain?

On a personal level, this stay was very formative, as it was the first time I’d gone abroad alone and for such a long time. Living in a foreign country was a completely different and enriching experience, as my daily life was very different from the one I had in France. Living in an environment where nobody spoke my language, and where it was sometimes difficult for me to understand exchanges in the street, was both disconcerting and stimulating, prompting me to reflect on my place in the world. This immersion enabled me to considerably improve my English communication skills, thanks in particular to the numerous exchanges with international students and Swedes. I’ve managed to make a lot of friends, particularly at KTH, but especially with the Stockholm University Orchestra. Swedes can be quite reserved towards international students and it wasn’t always easy to integrate into extra-curricular activities. However, my involvement in the orchestra offered me a unique opportunity to build lasting relationships, which were maintained throughout the year. It was also my first time living in a city the size of Stockholm. This could sometimes be a little unsettling, but the wealth of activities on offer and the excellent public transport network enabled me to discover many facets of this dynamic metropolis. Last but not least, my stay here strengthened my ability to adapt to situations where information is incomplete, and opened up the prospect of future assignments or professional opportunities abroad.

How would you sum up your year in Sweden?

The main academic highlights of my year were the group projects carried out in the various courses, as well as the exams, which greatly improved my vocabulary and fluency in both spoken and written English. On a cultural level, I was particularly impressed by Stockholm’s major events, such as Walpurgis Night, Nobel Prize week and the Christmas markets, as well as by my various trips, notably to Lapland and Norway. On a personal note, I‘ll never forget the various performances I’ve given with my orchestra, and all the convivial moments I’ve shared with its members.

My training in applied mathematics made a significant contribution to my engineering training, providing me with in-depth knowledge and indispensable mathematical tools in a wide range of engineering applications, in particular optimization and CFD techniques applied to the aerospace sector.

What’s next for you?

From now on, I’m returning to ISAE-SUPAERO for my final year of the engineering curriculum. I’ll be taking courses in the OTSU program, specializing in Earth Observation. I’ll also be taking the MSXS field, with a specialization in deterministic mathematics, to establish continuity with the training I received at KTH. I’ll also be taking MSXS with a specialization in deterministic mathematics, to establish continuity with the training I received at KTH.

Then I ‘d like to find an end-of-study internship that would enable me to apply both my skills in applied mathematics that I’ve been able to develop at KTH, and my skills as an aerospace engineer that I’ll be continuing to develop at ISAE-SUPAERO. This end-of-study internship would also serve as a Degree Project to conclude my training at KTH. This project involves writing a final report that will be published on the school’s website.

In the end, this stay has given me enormous academic, cultural and personal benefits. It gave me many skills that I will no doubt be able to apply throughout my career. I would like to express my deepest gratitude to the ISAE-SUPAERO Foundation, whose support was indispensable to this experience, which was particularly enriching on both a personal and professional level.

Any final words?

I would like to warmly thank the Fondation ISAE-SUPAERO for its trust and financial support. Your contribution to the development of students in this type of project is remarkable and personally enabled me to make the most of my stay in Sweden.