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Discrete Versions of Stokes’ Theorem Based on Families of Weights on Hypercubes

  • Gilbert Labelle
  • Annie Lacasse
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5810)

Abstract

This paper generalizes to higher dimensions some algorithms that we developed in [1,2,3] using a discrete version of Green’s theorem. More precisely, we present discrete versions of Stokes’ theorem and Poincaré lemma based on families of weights on hypercubes. Our approach is similar to that of Mansfield and Hydon [4] where they start with a concept of difference forms to develop their discrete version of Stokes’ theorem. Various applications are also given.

Keywords

Discrete Stokes’ theorem Poincaré lemma hypercube 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Gilbert Labelle
    • 1
  • Annie Lacasse
    • 2
  1. 1.Laboratoire de Combinatoire et d’Informatique MathématiqueUQAMMontréalCanada
  2. 2.Laboratoire d’Informatique, de Robotique et de Microélectronique de MontpellierMontpellier Cedex 5France

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