Spotlight on Young Researchers: Martin Řehoř


In industry, computer simulations and optimizations are established approaches to inform and improve engineering designs. As part of his Industrial Fellowship, Postdoc Martin Řehoř works on numerical solvers that could help solve design problems that involve the processing of fluids.

Thanks to computer simulations, engineers can digitally design, virtually build, validate and test new products prior to expensive physical prototyping. However: manufacturing and product engineers innovate on new processes and product lines faster than new simulation tools are commercialized. This has led to an innovation gap and a continuous need to bring new simulation methodologies to the market.

Czech national Martin Řehoř is helping tackle this through his Industrial Fellowship, as part of which he works on a research project involving both an industry partner (Rafinex) and an academic partner (University of Luxembourg). Rafinex (founded by FNR AFR PhD ‘alumni’ André Wilmes), a company offering simulation and optimization tools that account for the real-life variability in engineering systems, rather than just considering idealized conditions, has the role of Martin’s host institution in the project.

Martin Řehoř

HPC-boosted algorithms

“My research focuses on physical processes where a fluid flows inside a domain (container, channel, etc.). It is not only about the fluids that everyone knows from everyday life, such as air and water, but also about more complex substances including glass and rubber (in their molten states),” Martin explains, adding:

”The behaviour of such materials can be described mathematically via systems of partial differential equations (PDEs). Each such system poses a challenging problem for mathematicians who are striving to analyze its solution – if it exists!”

“In practice, we use sophisticated numerical algorithms to get an approximation of the solution with the aid of high-performance computing (HPC) facilities.”

One of the objectives of Martin’s current research project is to develop numerical solutions for complicated industrial problems without unnecessary limiting assumptions, thus using high-fidelity physics along with cutting-edge material models.

“In my current role at Rafinex, I am working on the development and implementation of robust numerical solvers that have a potential to be used in optimization tools for design problems involving the processing of fluids (melt extrusion additive manufacturing, injection molding, etc.).”

A challenge: nonlinear terms

Partial differential equations (PDEs) describing the behaviour of complex fluid-like materials are coupled systems containing many challenging nonlinear terms, which makes them extremely difficult to solve numerically in complicated domains such as injection molding cavities. As a consequence, a number of simplifying assumptions is often applied to make the computer simulations feasible, even though it is known that it considerably increases the reliability and predictive power of the results by adding a missing piece of information. Such simplifications may have been introduced as part of a method due to constraints on computational resources in the past, but they are no longer relevant in the age of cloud-based HPC accessibility.


Projects where academic research join forces with industry are a win-win: industry gets access to the researchers’ expertise, while researchers often explain a big joy for them in such a partnership is being able to see their work have a direct impact. Martin gives a concrete example of why such a partnership is beneficial for industry and scientists:

“The float glass forming process and the extrusion of rubber compounds are typical examples of industrial processes where it is nearly impossible to do on-the-fly experiments. Tuning the operational conditions in order to improve the overall quality of the end product is too risky and expensive to do. Customers increasingly ask for greater automation of the virtual design, build, validate and test cycle; requesting optimised answers rather than just normal simulations.”

“However, very tight deadlines often do not allow manufacturers to spend enough effort investigating the most recent methodologies, let alone their costly implementation. Obviously, this opens the door for promising collaborations between  researchers based either at public institutions, or at companies with strong R&D background. From the other point of view, I can hardly imagine a researcher who would not enjoy working on real-life problems/applications!”

More about what it is like work with an industry partner/Rafinex

“Rafinex is a small start-up company working on a remote basis with its co-founders and representatives based in Luxembourg, United Kingdom and Germany. I am based at the Luxembourg-City Incubator (LCI), a place with an unmistakable working atmosphere, giving me great exposure to other dynamic companies involved in Luxembourg’s startup ecosystem. There I have the chance to regularly meet with the CEO of the company, Dr. André Wilmes.”

“We discuss both R&D and business related topics with all three remaining representatives of Rafinex during our daily virtual meetings. Thanks to this I have been constantly given opportunities to take an active part in formulating the company’s vision. I am glad to help shape a young company created by young researchers for young researchers, focused on scientific excellence and business impact.”

“For developing simulations discussed above, I have been using the FEniCS computing platform (, which is being co-developed at the University of Luxembourg. I regularly take advantage of the opportunity to go and discuss various technical issues face to face with the developers including Dr. Jack Hale, a Research Scientist at the University and a member of the advisory board for my current research project.”

Working in industry vs academia

The current project with Rafinex is Martin’s first on-site experience in a competitive industrial environment – a hugely different experience to working in an academic setting. Martin explains where he sees the main contrasts:

“Let us say, hypothetically, that I invented a novel numerical method. In academia, I would publish the results in a journal and the method would become appreciated and recognized by a narrow group of experts working in the same field, maybe. This step can already make me happy and satisfied. However, this is not the end of the story in industry, where I have to take that method, turn it into a simulation tool that works in a variety of test case scenarios and persuade the customers about its business advantages.”

“The last step is especially important as it has the potential to make the group of experts who will recognize and appreciate the original idea a bit wider. I personally enjoy finding myself somewhere between these two worlds, as it gives me the opportunity to mediate the transfer of the existing state-of-the-art scientific methods to the end users who can directly benefit from them.”

“Luxembourg’s innovation potential is huge”

R&D in the field of computational mathematics is an expensive area – Martin explains that not many places in Europe still support dedicated numerical math departments, but Luxembourg does:

“With the University being founded only in 2003, it is amazing what great progress Luxembourg has made in its R&D activities over the last two decades. As one of the co-founders of the EuroHPC Joint Undertaking, Luxembourg is putting a lot of emphasis on digital knowledge processes of the future, and now has invested in Meluxina, which is of direct interest to my research. So, I simply believe that Luxembourg’s innovation potential is huge.”

From conference participant to researcher in Luxembourg

Martin first visited Luxembourg in 2017 to attend a conference, which led to him returning later in the year – this time to take up a postdoc position, a collaboration between the University of Luxembourg and Goodyear S.A.:

“During the conference I started chatting with Dr. Hale from the University of Luxembourg and he mentioned that he had a postdoctoral position that was a good match for my skills. So, I came specifically to Luxembourg in late 2017 to start this position funded through the FNR BRIDGES project SLIPEX. Near the end of this project, I knew that I wanted to stay and work in R&D in Luxembourg, but I wanted to make a transition from academia to industry.”

“During his PhD at Imperial College London, Dr. Hale shared an office with Dr. André Wilmes, who would go on to found Rafinex S.à r.l. in Luxembourg in 2017. After some informal discussions together in early 2019, we realized that I could make a real contribution to Rafinex’s R&D work. So, with the valuable funding support of the FNR Industrial Fellowship programme I can now make a contribution at this exciting new company.”

“It is of note that the FNR has previously supported fellowships for Dr. Wilmes (AFR PhD), Dr. Hale (AFR Marie Curie Postdoctoral) and myself (Industrial Fellowship)! So without the FNRs support, I am certain that we would not be here now in Luxembourg working together!”

More about Martin Řehoř

Martin’s research interests are rooted in computer simulation and optimization of challenging physical processes encountered in a variety of industries ranging from automotive, through food processing, to manufacturing of glass.

“I have been working in academia since 2013; in the beginning as a PhD student, jointly at Charles University in Prague and Heidelberg University, and more recently as a postdoctoral researcher at the University of Luxembourg. All of my research projects thus far have been driven by the challenging demands of industrial partners.

“During my PhD, I was given the opportunity to work with GLASS SERVICE, a.s. ( as a member of the research group at the department of mathematical modelling at Charles University. We worked on large-scale simulations of the float glass forming process, where molten glass cools over a bath of molten tin, forming perfectly flat and uniform sheets of glass. This is a difficult problem to simulate, as it involves tracking a highly complex and evolving interface between the air, molten glass, and molten tin. A better quantitative understanding of this process is necessary for improving the production quality and rates.”

“During my postdoctoral project at the University of Luxembourg, in conjunction with Goodyear S.A., I tried to understand and simulate slip in industrial extrusions of flowing rubber compounds. Again, this is a difficult problem to simulate due to the complexity of the viscoelastic behaviour of rubber, and the interactions between the rubber and the wall of the extruder. Again, a better quantitative understanding of these processes is necessary for improving production quality and rates.”

Role models

“I had the chance to meet many fantastic scientists from and outside academia, and the list of people who I do find inspirational is still expanding. If I tried to name some of them I would feel bad not mentioning all of them.”

“I have always enjoyed working and interacting with those people no matter whether it was at the department of mathematical modelling at Charles University, or at the interdisciplinary research center for scientific computing at Heidelberg University, or here in Luxembourg at the University and Rafinex. In any case, this would not have been possible if I had not met my math teachers at the secondary school. I think it was the passion with which they explained challenging mathematical problems that motivated me to become a researcher.”

Martin Řehoř


About Spotlight on Young Researchers

Spotlight on Young Researchers is an FNR initiative to highlight early career researchers across the world who have a connection to Luxembourg. The campaign is now in its 5th year, with 60+ researchers already featured. Discover more young researcher stories below.


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