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Research Training Group "Scientific Computation"
PaSCo GK

Research

Scientific Computation encompasses mathematical modeling, the design of numerical methods and algorithms as well as their implementation for problems from all areas of science and their applications. It also includes basic research on algorithms and complexity on the one hand and the design and implementation of software for scientific problems on the other hand.

Principal aim of the DFG Research Training Group is the development of efficient solution methods in the field of Scientific Computation, guided by different real world problems from science and engineering. In accordance with this aim, all research projects are interdisciplinary, with mathematics and computer science as basic fields, but with a strong component from engineering and the natural sciences.

In contrast to approaches in Scientific Computation where one seeks cooperation either between mathematicians and applied scientists or between computer scientists and applied scientists, the DFG Research Training Group foster close cooperation between all three fields. Thus the whole gamut is covered from the application problem through mathematical modeling and the development of efficient algorithms down to the numerical solution.

The research projects of the DFG Research Training Group are interdisciplinary and fall within the following areas:

Dynamical Processes

In the field of Dynamical Processes we concentrate on the analysis of systems which are networked or have complex dynamics. A lot of topics in this field are oriented on applications from the Natural, Engineering or Computer Sciences. Modern techniques of algorithms should be connected with the numerical treatment of dynamical systems to combine numerical analysis and computer science. The aim is to develop new and efficient (numerical) methods for the analysis of the qualitative behavior of dynamic systems.

Project Suggestions:

1.1The control of invariant measures
Supervision: Dellnitz, Junge, Wallaschek
1.2Partitioning of time-dependent graphs
Supervision: Dellnitz, Meyer auf der Heide, Monien
1.3Particle filter and transfer operators
Supervision: Junge, Dellnitz, Häb-Umbach
1.4Complexity Theory and dynamical systems
Supervision: Bürgisser, Dellnitz, von zur Gathen
1.5Computability of idealized physical models
Supervision: Bürgisser , Frauenheim, Meyer auf der Heide
1.6Compact networks of mobile and autonomous mechatronic systems - strategies and dynamics
Supervision: Dellnitz, Wallaschek, Junge
1.7Parallel visualization of three dimensional adaptive flow data
Supervision: Monien, Dellnitz
1.8Electron conduction in molecular wires in a non-equilibrium Green's
function formalism
Supervision: Frauenheim, Monien
1.9Development of collision avoidance strategies for autonomous driving
Supervision: Dellnitz, Meyer auf der Heide, Wallaschek
1.10Analysis of communication processes by systems of differential equations
Supervision: Dellnitz, Meyer auf der Heide, Monien
1.11Load balancing methods accounting for structural and spectral network properties
Supervision: Monien, Dellnitz
1.12Complexity of computation of Nash equilibria
Supervision: Monien, Dellnitz
1.13Dynamical systems and pseudo random numbers
Supervision: Dellnitz, von zur Gathen, Meyer auf der Heide
Development of Algorithms and Complexity Theory

In the field of Algorithms and Fundamentals of Complexity Theory we focus on the following topics: complexity theoretic treatment of computation models over the reals, complexity reduction, and algorithms for noisy data. The first topic is related to algorithmic geometry, computer graphics, and complexity theoretic treatment of dynamical systems. The other two topics combine algorithmic fundamental research with applications to e.g. speech recognition.

Project Suggestions:

2.1
Uniform versus non-uniform computation models over the reals
Supervision: Meyer auf der Heide, Bürgisser, von zur Gathen
2.2Computational complexity of topological invariants
Supervision: Bürgisser, Meyer auf der Heide
2.3Discrete models for computations over the reals
Supervision: Bürgisser, Meyer auf der Heide
2.4Lower bounds for streaming algorithms
Supervision: Sohler, Bürgisser
2.5Complexity of lattice problems
Supervision: Blömer, von zur Gathen
2.6Lower Bounds for computations over the integers
Supervision: Meyer auf der Heide, Bürgisser, Blömer
2.7Dynamical streaming algorithms in geometry
Supervision: Sohler, Meyer auf der Heide
2.8Dimension reduction methods to increase classification rates
Supervision: Häb-Umbach, von zur Gathen, Meyer auf der Heide
2.9Efficient model reduction for Markov processes
Supervision: Blömer, Häb-Umbach, Sohler
2.10Streaming algorithms for matchings in graphs
Supervision: Meyer auf der Heide, Sohler
2.11Intelligent sampling to determine the free energy of molecules using
coarse decompositions of the phase space
Supervision: Dellnitz, Frauenheim
2.12Condition numbers and smoothed analysis
Supervision: Bürgisser, Sohler, Monien
2.13Classification of point sets
Supervision: von zur Gathen, Meyer auf der Heide, Häb-Umbach
2.14Improvement of speech quality using particle filters
Supervision: Häb-Umbach, Blömer

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