{"responseHeader":{"status":0,"QTime":3,"params":{"q":"{!q.op=AND}id:\"707618\"","hl":"true","hl.simple.post":"","hl.fragsize":"5000","fq":"!embargo_tdt:[NOW TO *]","hl.fl":"ocr_t","hl.method":"unified","wt":"json","hl.simple.pre":""}},"response":{"numFound":1,"start":0,"docs":[{"date_modified_t":"2010-10-19","ark_t":"ark:/87278/s6jw8zkp","date_digital_t":"2010-10-19","setname_s":"ir_uspace","restricted_i":0,"department_t":"Computing, School of","format_medium_t":"application/pdf","creator_t":"Bhatia, Harsh; Jadhav, Shreeraj Digambar; Norgard, Greg; Bremer, Peer-Timo; Pascucci, Valerio","identifier_t":"ir-main/14793","bibliographic_citation_t":"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.","mass_i":1515011812,"publisher_t":"University of Utah","description_t":"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.","rights_management_t":"(c) Harsh Bhatia, Shreeraj Jadhav, Greg Norgard, Peer-Timo Bremer, Valerio Pascucci","title_t":"Helmholtz-Hodge Decomposition of vector fields on 2-manifolds","ocr_t":"Results d h r Decomposition1 Helmholtz-Hodge Decomposition of vector fields on 2-manifolds Harsh Bhatia, Shreeraj Jadhav, Greg Norgard, Peer-Timo Bremer, Valerio Pascucci 1. K Polthier, E Preuβ : Variational Approach to Vector Field Decomposition 2. K Polthier, E Preuβ : Identifying Vector Field Singularities Using a Discrete Hodge Decomposition References What ? Decomposition of a vector field into conservative and rotational components 1. Conservative Component ( d ) has zero rotation. 2. Rotational Component ( r ) has zero divergence. 3. Harmonic Component ( h ) has zero divergence and zero rotation. 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. How ? Discrete HH decomposition can be calculated as a global energy minimization over the Domain2 1. Quadratic energy functional to determine u 2. Quadratic energy functional to determine w 3. Harmonic component 0 Why ?","id":707618,"publication_type_t":"poster","parent_i":0,"type_t":"Text; Image","thumb_s":"/c6/80/c680a7b437c8bb7233cca57abe75d039dfb98cf4.jpg","oldid_t":"uspace 5500","metadata_cataloger_t":"dw","format_t":"application/pdf","modified_tdt":"2013-09-25T00:00:00Z","school_or_college_t":"Scientific Computing and Imaging Institute","language_t":"eng","file_s":"/8d/86/8d86cb5fe3fb7e9ebb121b2dda3d70d108b51f64.pdf","format_extent_t":"446,587 bytes bytes","created_tdt":"2012-07-30T00:00:00Z","_version_":1642982699581833216}]},"highlighting":{"707618":{"ocr_t":[]}}}