About MaCS: Mathematics of Computational Science

Text: Matthias Schlottbom

MaCS is the abbreviation of ‘Mathematics of Computational Science’, and we are working on various mathematical aspects of numerical methods. These range from the development of fast numerical solvers for very large systems of equations over error analysis of numerical methods to the solution of inverse problems. We apply our methods in many fields from physics and engineering, e.g., in the design of metamaterials, biomedical imaging, or subsurface imaging. If you are interested in that, let me invite you to discuss with us possible internships or final projects.

To get a better idea, here is a brief overview of our group:

• Tugce Akkaya: The research question that her PhD work seeked to answer is "What is the damping properties of rainwind induced oscillations of inclined cables?" at the Mathematical Physics department. One of her courses is ‘Introduction to PDEs’ (B-AM). She is currently appointed as Teaching & Learning Fellow for our faculty.

• Fleurianne Bertrand: Her work is strongly motivated by challenges related to the modeling and the numerical simulation of physical phenomena and it contributes to the development of numerical schemes for the simulation of problems in continuum mechanics. A significant part of her research is devoted to the investigation of structure preserving finite element methods. In this framework she also studies abstract properties of finite element spaces. In the master, you’ll meet her in the courses Scientific Computing and Finite Element Methods.

• Philip Lederer: You may not have encountered him yet, because he is going to join us in March 2023. His main interest lies in the numerical analysis of partial differential equations (PDEs) describing the motion of fluids. Next to his research on incompressible flows, such as the motion of water, he recently started to investigate also acoustic phenomena in compressible flows. For this, he develops new finite element methods and algorithms to approximate the solutions.

• Carlos Pérez Arancibia: You can probably recognize this long name already, if you have taken Analysis I and II (B-AM) during this academic year. Carlos' research interests lie at the intersection of wave phenomena, boundary integral equations, and high-order PDE solvers, with applications in layered and periodic media scattering, waveguides, and inverse design of optical metamaterials, among others.

• Jaap van der Vegt: His main interest is in the development, theoretical analysis, and application of finite element methods for PDEs with applications in physics such as wave problems in electromagnetics, fluids, and solids. Although his formal retirement is approaching, he will stay active in mathematics and continue to contribute to the research of our group and at USTC in China.

• Matthias Schlottbom: My research is in the context of analysis and numerical analysis for (high-dimensional) PDEs, with applications, e.g., in optics or medical imaging. To solve these PDEs numerically, I do research into accurate low-order models as well as finite elements. Having fast, accurate and robust numerical methods at hand, I am also interested in data assimilation and the solution of inverse problems, such as optical tomography. You may meet me in the Numerical Mathematics class (B-AM), or the master classes PDEs or Numerical Methods for PDEs.

As you have noticed, the words ‘analysis’ and ‘applications’ appear frequently, and it is true that our work is often carried out in collaboration with others, for instance, with colleagues from the Applied Mathematics Department, other faculties, or even other universities.

I hope this short article gives you a first impression of MaCS and the topics we are working on. If you do want to know more, do not hesitate to knock my door or to send me an e-mail.