Research
The Seminar for Applied Mathematics (SAM) is committed to conducting fundamental research in the development and mathematical analysis of efficient discretizations for problems in engineering and the sciences as well as their implementation on supercomputers.
Research at SAM combines rigorous mathematical analysis and algorithmic developments inspired and driven by concrete applications. It encompasses the derivations and analysis of mathematical models, investigations of stability, convergence, and structure of discretizations, and considerations on complexity and efficient implementation of numerical methods, including those on massively parallel, ultra-large scale high performance computing platforms.
Focus on applications at SAM involves a keen interest in interdisciplinary research, which is reflected in the numerous collaborations with scientists outside mathematics and joint projects with the industry.
Current research topics include:
- Finite element, finite volume, boundary element methods
- Structure preserving discretizations for partial differential equations
- Deterministic numerical methods for kinetic equations
- Numerical uncertainty quantification (UQ)
- Analysis and numerical methods for stochastic ODEs and PDEs
- Multi-scale approximation and representations
- Multi-level Monte-Carlo and quasi Monte-Carlo methods for UQ
- Tensor structured numerical methods for PDEs in high dimensions
- Computational quantum mechanics
- Computational wave propagation
- Hybrid and super-resolution (medical) imaging
- Computational nano-optics and plasmonics
- Computational Astrophysics
- Deep Learning in data-driven numerical PDE solution
Research results of researchers at SAM are documented in the institute's report series.