Participating working groups - Mathematics
This page lists all working groups of the Department for Mathematics and Computer Science / Division Mathematics whose research focuses fit the ideas of the key profile area "Intelligent Methods for Earth System Sciences".
The AG Gassner deals with the construction, analysis and efficient implementation of numerical methods for the solution of nonlinear processes describing strong advection, such as compressible turbulent flows or plasmas. For this purpose, so-called structure-preserving methods are developed, which exactly reproduce special properties of the mathematical problem (conservation, entropy, kinetic energy). The focus is also on the efficient implementation of these methods on massively parallel high performance computers, e.g., in the open source simulation package
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The research group AG Klawonn works on the development of efficient numerical methods for the simulation of problems from computational science and engineering. This comprises the development of efficient algorithms, their theoretical analysis, and the implementation on large parallel computers with up to several hundreds of thousands of cores. A special focus in the applications is currently on problems from biomechanics/medicine, structural mechanics, and material science.
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The research topics of AG Kunoth are:
- Numerical Analysis of PDEs: Wavelet and multiscale techniques for the numerical solution of elliptic partial differential equations, in particular: treatment of boundary conditions and boundaries, fictitious domain methods, preconditioning, least squares methods, adaptive methods.
- Numerical Analysis of Control Problems: above approaches for the numerical solution of control problems with PDE constraints.
- Approximation Theory: Construction of biorthogonal wavelets and multiwavelets on bounded domains; Approximation of Digital Terrain Elevation Data; Optimal encoding; Approximation by ridge functions.
- Computer Aided Geometric Design, Statistics: Curve and surface fitting of nonuniformly distributed data and data with outliers by adaptive wavelets with smoothing
- Numerical Analysis of Inverse Problems: Mathematical modelling and numerical simulations for the lithographic generation of nanostructures
- Numerical Analysis of Problems in Computational Finance: Option pricing computations by multiscale methods
- Numerical Analysis of Problems in Micromagnetics: Simulation of thin-film ferromagnetic elements
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