The group "Numerical Analysis and Computational Science" deals with the development, analysis and implementation of methods for solving problems of practical relevance. The focus is on the numerical treatment of integral equations and partial differential equations.
The complexity for the treatment of integral equations is dominated by the generation and the solution of the densly populated system matrix. One major research direction of the group is the development of automatically adapted numerical integration techniques to reduce the complexity for the generation of the matrix elements. Alternative representations of discrete integral operators by Cluster techniques will reduce memory- and computing reqirements for the numerical treatment of integral equations from O(N²) (N=number of degree of freedom) to O(N log N) respectively O(N). The further development of this technique, also to time depending wave and electromagnetic problems, and application to practical problems (geodesy, population dynamics, fluid mechanics,...) is a research field of the research group.
The development of flexible discretisation methods for boundary value problems on complicated domains (e.g. lakes) or with complicated coefficients is a major research direction in the research group. Keywords: Composite Finite Elements, Multi-Grid methods, Coarsening Operators. For the evaluation of the methods, the question for efficient implementations also plays a substantial role. Insights from analysis and computer science play an important part for the development of this numerical methods.