Helmholtz-Hodge Decomposition of vector fields on 2-manifolds

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Publication Type poster
School or College Scientific Computing and Imaging Institute
Department Computing, School of
Creator Bhatia, Harsh; Jadhav, Shreeraj Digambar; Norgard, Greg; Bremer, Peer-Timo; Pascucci, Valerio
Title Helmholtz-Hodge Decomposition of vector fields on 2-manifolds
Description A Morse-like Decomposition ? - Morse-Smale decomposition for gradient (of scalar) fields is an interesting way of decomposing the domain into regions of unidirectional flow (from a source to a sink ). - But works for gradient fields, which are conservative (irrotational), only. - Can such a decomposition and analysis be extended to generic (consisting rotational component) vector fields ? - Can we extract the rotational component out from generic vector fields ? Feature Identification ? - Analysis on the decomposed components of fields is simpler. eg Identification of critical points in the potentials of the two components is easy. Topological Consistency ? - Is there any relation between the topology of the components and the topology of the original field ? Limitation - So far, HH Decomposition exists only for piece-wise constant vector fields. Such a decomposition for piece-wise linear fields is desirable.
Type Text; Image
Publisher University of Utah
Language eng
Bibliographic Citation Bhatia, H., Jadhav, S. D., Norgard, G., Bremer, P-T., & Pascucci, V. (2010). Helmholtz-Hodge Decomposition of vector fields on 2-manifolds. University of Utah.
Rights Management (c) Harsh Bhatia, Shreeraj Jadhav, Greg Norgard, Peer-Timo Bremer, Valerio Pascucci
Format Medium application/pdf
Format Extent 446,587 bytes bytes
Identifier ir-main/14793
ARK ark:/87278/s6jw8zkp
Setname ir_uspace
Date Created 2012-07-30
Date Modified 2021-05-06
ID 707618
Reference URL https://collections.lib.utah.edu/ark:/87278/s6jw8zkp
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