Efficient Morse decompositions of vector fields Public Deposited

http://ir.library.oregonstate.edu/concern/technical_reports/z890rv461

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  • 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 [tau] 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 effectively, we present an adaptive approach in constructing better approximations of the images of triangles in the meshes used for simulation. These techniques result in fast and efficient MCG construction. We demonstrate the efficacy of our technique on various examples in planar fields and on surfaces including engine simulation data.
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  • description.provenance : Submitted by Laura Wilson (laura.wilson@oregonstate.edu) on 2012-12-12T17:28:37Z No. of bitstreams: 1 2007-27.pdf: 2022238 bytes, checksum: dc10d0a9deaa73198b78bd11de7b77ca (MD5)
  • description.provenance : Made available in DSpace on 2012-12-12T17:30:32Z (GMT). No. of bitstreams: 1 2007-27.pdf: 2022238 bytes, checksum: dc10d0a9deaa73198b78bd11de7b77ca (MD5) Previous issue date: 2007
  • description.provenance : Approved for entry into archive by Laura Wilson(laura.wilson@oregonstate.edu) on 2012-12-12T17:30:32Z (GMT) No. of bitstreams: 1 2007-27.pdf: 2022238 bytes, checksum: dc10d0a9deaa73198b78bd11de7b77ca (MD5)

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