@ARTICLE{GaPrRuTeWeWi01,
author = {Garcke, H. and Preu{\ss}er, T. and Rumpf, M. and Telea, A. and Weikard,
U. and van Wijk, J.},
title = {A Phase Field Model for Continuous Clustering on Vector Fields},
journal = {IEEE Transactions on Visualization and Computer Graphics},
year = {2001},
volume = {7},
pages = {230--241},
abstract = {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.},
pdf = {http://numod.ins.uni-bonn.de/research/papers/public/GaPrRuTeWeWi01.pdf}
}