Efficient Morse Decompositions of Vector Fields

Vector field analysis plays a crucial role in many engineering applications, such as weather prediction, tsunami and hurricane study, and airplane and automotive design. Existing vector field analysis techniques focus on individual trajectories such as fixed points, periodic orbits and separatrices which are sensitive to noise and errors introduced by simulation and interpolation. This can make such vector field analysis unsuitable for rigorous interpretations. In this paper, we advocate the use of Morse decompositions, which are robust with respect to perturbations, to encode the topological structures of the vector field in the form of a directed graph, called a Morse decomposition connection graph (MCG). While an MCG exists for every vector field, it need not be unique. We develop the idea of a map, which decouples the MCG construction process and the configuration of the underlying mesh. This, in general, results in finer MCGs than mesh-dependent approaches. To compute MCGs effec...

• Type: Journal
• Year: 2008
• Where: TVCG
• Authors: Guoning Chen, Konstantin Mischaikow, Robert S. Laramee, Eugene Zhang
• Keywords: Morse Decomposition, TVCG 2008, Vector Field, Vector Field Analysis