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Abstract

In recent years, simulations have steadily replaced real world experiments in science and industry. Instead of performing numerous arduous experiments in order to develop new products or test a hypothesis, the system to be examinded is described by a set of equations which are subsequently solved within the simulation. The produced vector fields describe the system's behavior under the conditions of the experiment. While simulations steadily increase in terms of complexity and precision, processing and analysis are still approached by the same long-standing visual techniques. However, these are limited by the capability of the human visual system and its abilities to depict large, multi-dimensional data sets.

In this thesis, we replace the visual processing of data in the traditional workflow with an automated, statistical method. Cluster algorithms are able to process large, multi-dimensional data sets efficiently and therefore resolve the limitations we faced so far. For their application to vector fields we define a special feature vector that describes the data comprehensively. After choosing an appropriate clustering method, the vector field is split into its features.

Based on these features the novel flow graph is constructed. It serves as an abstract representation of the vector field and gives a detailed description of its parts as well as their relations. This new representation enables a quantitative analysis and describes the input data. Additionally, the flow graphs are comparable to each other through a uniform description, since techniques of graph theory may be applied. In the traditional workflow, visualization is the bottleneck, because it is built manually by the user for a specific data set. In consequence the output is diminished and the results are likely to be biased by the user. Both issues are solved by our approach, because both the feature extraction and the construction of the flow graph are executed in an un-supervised manner.

We will compare our newly developed workflow with visualization techniques based on different data sets and discuss the results. The concluding chapter on the similarity and comparison of graphs applies techniques of graph theory and demonstrates the advantages of the developed representation and its use for the analysis of vector fields using flow graphs.