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Discrete Exterior Calculus

Desbrun, Mathieu and Hirani, Anil N. and Leok, Melvin and Marsden, Jerrold E. (2005) Discrete Exterior Calculus. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20190924-075138788

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Abstract

We present a theory and applications of discrete exterior calculus on simplicial complexes of arbitrary finite dimension. This can be thought of as calculus on a discrete space. Our theory includes not only discrete differential forms but also discrete vector fields and the operators acting on these objects. This allows us to address the various interactions between forms and vector fields (such as Lie derivatives) which are important in applications. Previous attempts at discrete exterior calculus have addressed only differential forms. We also introduce the notion of a circumcentric dual of a simplicial complex. The importance of dual complexes in this field has been well understood, but previous researchers have used barycentric subdivision or barycentric duals. We show that the use of circumcentric duals is crucial in arriving at a theory of discrete exterior calculus that admits both vector fields and forms.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/math/0508341arXivDiscussion Paper
ORCID:
AuthorORCID
Desbrun, Mathieu0000-0003-3424-6079
Record Number:CaltechAUTHORS:20190924-075138788
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190924-075138788
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:98817
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:24 Sep 2019 14:56
Last Modified:03 Oct 2019 21:44

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