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2014 | OriginalPaper | Chapter

Robust Detection of Singularities in Vector Fields

Authors : Harsh Bhatia, Attila Gyulassy, Hao Wang, Peer-Timo Bremer, Valerio Pascucci

Published in: Topological Methods in Data Analysis and Visualization III

Publisher: Springer International Publishing

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Abstract

Recent advances in computational science enable the creation of massive datasets of ever increasing resolution and complexity. Dealing effectively with such data requires new analysis techniques that are provably robust and that generate reproducible results on any machine. In this context, combinatorial methods become particularly attractive, as they are not sensitive to numerical instabilities or the details of a particular implementation. We introduce a robust method for detecting singularities in vector fields. We establish, in combinatorial terms, necessary and sufficient conditions for the existence of a critical point in a cell of a simplicial mesh for a large class of interpolation functions. These conditions are entirely local and lead to a provably consistent and practical algorithm to identify cells containing singularities.

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Title: Robust Detection of Singularities in Vector Fields
Authors: Harsh Bhatia
Attila Gyulassy
Hao Wang
Peer-Timo Bremer
Valerio Pascucci
Publisher: Springer International Publishing
Book: Topological Methods in Data Analysis and Visualization III
Print ISBN: 978-3-319-04098-1

Electronic ISBN: 978-3-319-04099-8

Copyright Year: 2014
DOI: https://doi.org/10.1007/978-3-319-04099-8_1

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