Cross-sectional team Mathematical Methods and Algorithms
The cross-sectional team (CST) "Mathematical Methods and Algorithms" deals with mathematical aspects of computer simulations. Mathematical modeling, development and improvement of numerical algorithms as well as their application are important ingredients to computer simulations of complex systems and processes. In order to broaden the methodological basis of computational science this team carries out research in all these different areas. The R&D activities are performed in close cooperation with researchers of JSC's other groups, especially the SimLabs, as well as academic and industrial partners outside JSC.
Numerical Algorithms for High Performance Computing
The development of numerical methods and algorithms which are of strategic importance in a wide range of application fields is a cornerstone of scientific computing. In order to make simulations more realistic the system size or the accuracy of the models has to be increased. In both cases the applications depend on powerful numerical algorithms which make efficient use of high performance computer architectures. Thus one focus of research in the CST team is the provision of efficient numerical core algorithms.
Some recent results and on-going work in this area are
- Research on parallel-in-time integration methods
- Research on partial differential equations
- Highly-scalable Fast Multipole Method for simulations of systems with trillions of particles
- Porting parallel mathematical software to new HPC systems, performance evaluation
Modeling and Simulation
Another focus of research is the application of mathematical methods to problems which cannot be successfully tackled with already existing solutions. The questions arise very often within collaborations with academic research groups inside and outside Forschungszentrum Jülich as well as from projects with industry. Current activities include the
We offer any kind of collaboration in the field of Statistics such as modeling and model fitting which leads to parameter estimation. Precisely, the construction of e.g. point estimators (parametric: method-of-moments, Maximum-Likelihood; percentile-matching; robust parametric: method-of-trimmed-moments), their numerical computations, and the investigation of their large-sample properties. Additionally, to assess the quality of fits, we use basic graphical tools (quantile-quantile plots), goodness-of-fit statistics (Kolmogorov-Smirnov and Anderson-Darling), and information criteria such as (negative log-likelihood, Akaike information criterion, Bayesian information criterion).
Interactions with SimLabs
The CST team "Mathematical Methods and Algorithms" collaborates with JSC's SimLabs wherever mathematical expertise helps to enable simulations for supercomputing.
Current cooperations include the SimLabs
- Plasma Physics
Topic: Lattice operators for periodic boundaries in 1D, 2D, 3D
- Molecular Systems
Topic: Adapting and optimizing the Fast Multipole Method (FMM) for new architectures and processors. FMM is part of the SCAFACOS library (scalable fast Coulomb Solvers).
Topic: Image segmentation and registration
- Highly scalable fluid and solid engineering (FSE)
Topic: Aeronautical simulation software for up-to-date architectures together with DLR