H. Garcke, T. Preußer, M. Rumpf, A. Telea, U. Weikard, and J. van Wijk.
A phase field model for continuous clustering on vector fields.
IEEE Transactions on Visualization and Computer Graphics,
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A new method for the simplification of flow fields is presented. It is based on continuous clustering. A well-known physical clustering model, the Cahn Hilliard model which describes phase separation, is modified to reflect the properties of the data to be visualized. Clusters are defined implicitly as connected components of the positivity set of a density function. An evolution equation for this function is obtained as a suitable gradient flow of an underlying anisotropic energy functional. Here, time serves as the scale parameter. The evolution is characterized by a successive coarsening of patterns - the actual clustering - during which the underlying simulation data specifies preferable pattern boundaries. We introduce specific physical quantities in the simulation to control the shape, orientation and distribution of the clusters, as a function of the underlying flow field. In addition the model is expanded involving elastic effects. Thereby in early stages of the evolution shear layer type representation of the flow field can be generated, whereas for later stages the distribution of clusters can be influenced.