Discrete Exterior Calculus

  title={Discrete Exterior Calculus},
  author={Anil N. Hirani and Melvin Leok and Jerrold E. Marsden},
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… CONTINUE READING
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Publications referenced by this paper.
Showing 1-10 of 24 references

Multidimensional Analysis and Discrete Models

A. A. Dezin
CRC Press, • 1995
View 6 Excerpts
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Kotiuga. Data structures for geometric and topological aspects of finite element

P.R.P.W. Gross
View 5 Excerpts
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PhD thesis, California Institute of Technology, • 2003

Discrete diffeomorphism groupoids and circulation conserving fluid integrators

S. Pekarsky, M. West
(in preparation), • 2003

On a variational complex for difference equations

E. L. Mansfield, P. E. Hydon
View 1 Excerpt

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N. Hirani
PhD thesis, California Institute of Technology, • 2002
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