Robust Detection of Singularities in Vector Fields

  • Harsh Bhatia
  • Attila Gyulassy
  • Hao Wang
  • Peer-Timo Bremer
  • Valerio Pascucci
Conference paper

DOI: 10.1007/978-3-319-04099-8_1

Part of the Mathematics and Visualization book series (MATHVISUAL)
Cite this paper as:
Bhatia H., Gyulassy A., Wang H., Bremer PT., Pascucci V. (2014) Robust Detection of Singularities in Vector Fields. In: Bremer PT., Hotz I., Pascucci V., Peikert R. (eds) Topological Methods in Data Analysis and Visualization III. Mathematics and Visualization. Springer, Cham

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.

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Harsh Bhatia
    • 1
    • 2
  • Attila Gyulassy
    • 3
  • Hao Wang
    • 3
  • Peer-Timo Bremer
    • 1
    • 2
  • Valerio Pascucci
    • 3
  1. 1.SCI InstituteUniversity of UtahSalt Lake CityUSA
  2. 2.Center for Applied Scientific ComputingLawrence Livermore National LaboratoryLivermoreUSA
  3. 3.SCI InstituteUniversity of UtahSalt Lake CityUSA

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