Computational Discrete Morse Theory for Divergence-Free 2D Vector Fields

  • Jan Reininghaus
  • Ingrid Hotz
Part of the Mathematics and Visualization book series (MATHVISUAL)


We present a simple approach to the topological analysis of divergence-free 2D vector fields using discrete Morse theory. We make use of the fact that the point-wise perpendicular vector field can be interpreted as the gradient of the stream function. The topology of the divergence-free vector field is thereby encoded in the topology of a gradient vector field. We can therefore apply a formulation of computational discrete Morse theory for gradient vector fields. The inherent consistence and robustness of the resulting algorithm is demonstrated on synthetic data and an example from computational fluid dynamics.


Stream Function Gradient Vector Morse Theory Importance Measure Morse Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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We would like to thank David Günther, Jens Kasten, and Tino Weinkauf for many fruitful discussions on this topic. This work was funded by the DFG Emmy-Noether research programm. All visualizations in this paper have been created using AMIRA – a system for advanced visual data analysis (see


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Zuse Institute BerlinBerlinGermany

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