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@Article{RibeiroCampLope:2016:HeDeAn,
               author = "Ribeiro, Paula Ceccon and Campos Velho, Haroldo Fraga de and 
                         Lopes, H{\'e}lio",
          affiliation = "{Pontif{\'{\i}}cia Universidade Cat{\'o}lica Do Rio de Janeiro 
                         (PUC-Rio)} and {Instituto Nacional de Pesquisas Espaciais (INPE)} 
                         and {Pontif{\'{\i}}cia Universidade Cat{\'o}lica Do Rio de 
                         Janeiro (PUC-Rio)}",
                title = "Helmholtz-Hodge decomposition and the analysis of 2D vector field 
                         ensembles",
              journal = "Computers and Graphics (Pergamon)",
                 year = "2016",
               volume = "55",
                pages = "80--96",
                month = "Apr.",
             keywords = "Ensemble visualization, Helmholtz-Hodge decomposition, Uncertainty 
                         quantification, Vector fields.",
             abstract = "The Helmholtz-Hodge decomposition is a very useful instrument for 
                         vector field interpretation because it traditionally distinguishes 
                         conservative (curl-free) components from mass-preserving 
                         (divergence-free) components. In this work, we propose to use the 
                         Helmholtz-Hodge decomposition as a basic tool for the analysis of 
                         an ensemble of 2D vector fields. Given a vector field ensemble 
                         \ε, our approach firstly generates the corresponding 
                         curl-free, divergence-free, and harmonic component ensembles by 
                         using the Natural Helmholtz-Hodge decomposition to each vector 
                         field in \ε. With these ensembles in hand, our proposal not 
                         only quantifies, via a statistical analysis, how much each 
                         component ensemble is point-wisely correlated to the original 
                         vector field ensemble, but also allows to investigate the 
                         uncertainty of curl-free, divergence-free, and harmonic components 
                         separately. We test the proposed method with a synthetic vector 
                         field ensemble and with a simulated vector field ensemble.",
                  doi = "10.1016/j.cag.2016.01.001",
                  url = "http://dx.doi.org/10.1016/j.cag.2016.01.001",
                 issn = "0097-8493",
             language = "en",
           targetfile = "ribeiro_helmholtz.pdf",
        urlaccessdate = "29 nov. 2020"
}


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