Markus Faustmann

Markus Faustmann is a Senior Scientist at the Institute for Analysis and Scientific Computing (E 101) within the Faculty of Mathematics and Geoinformation at TU Wien. His research focuses on numerical methods for partial differential equations, with particular emphasis on fractional differential operators, finite element methods (FEM), boundary element methods (BEM), and hierarchical matrices. He has held roles including Senior Lecturer (2016-2021) and currently serves on the management team of TUForMath since 2023.

Education:

• PhD in Mathematics (Dr.techn.), TU Wien (2015)
• Dipl.-Ing. in Technical Mathematics, TU Wien (2009)
• Bachelor of Science in Technical Mathematics (B.Sc.), TU Wien (2008)

Research Interests: His work addresses non-local operators, elliptic regularity theory, and efficient numerical techniques for fractional PDEs. He develops and analyzes methods like hp-FEM and matrix compression strategies to tackle fully populated matrices arising from non-local problems. Recent projects include FEM-BEM coupling for fractional diffusion and exponential convergence analysis of hp-FEM.

Awards:

• TU Best Teacher Award 2022
• TU Best Paper Award 2022

Teaching & Advising: Faustmann teaches courses such as Nonlocal Operators and Numerical Methods for PDEs. He has supervised numerous students in master's theses (e.g., Paul Dunhofer, Tobias Slowiak) and bachelor's projects (e.g., Lukas Sichert, Paul Lucan). His seminars cover topics like randomized algorithms and differential equations.

Labs/Teams: Active in the TUForMath initiative and collaborates on projects involving adaptive FEM for fractional operators and H-matrix approximations.