Geometrica

Discrete differential geometry

with 6 comments

Various communities of researchers have thought about this class of problems; there are results scattered through journals on image processing, geometric mechanics, numerical analysis, graph theory, machine learning, general relativity (and more?). Besides its use in various domains of application, discrete geometry also provides fresh insights into classical, continuous geometry. (See, e.g., Regge’s discussion of Bianchi identities in his original paper on Regge calculus.)

Discrete exterior calculus, cohomology, etc.

Discrete Riemannian geometry, connections, etc.

Discrete spectral geometry

  • References on graph laplacians, etc.

Convergence of discrete geometric quantities to their continuous counterparts.

  • Add references.

Discrete geometric mechanics, discrete field theory

General links

People

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Written by mkz

March 29, 2010 at 10:04 pm

Posted in Uncategorized

6 Responses

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  1. I removed the post dedicated to Marsden’s talk a few days ago. You might want to update your post and replace this (broken) link with the following:

    Jerrold Marsden on Discrete Mechanics and Optimal Control

    Since you seem to be a physicist, you may find it interesting to take a look at Eric Forgy’s PhD thesis:

    Differential Geometry in Computational Electromagnetics [pdf]

    Rod Carvalho

    March 30, 2010 at 12:31 am

  2. The 2nd URL is obviously wrong. The right one is:

    http://phorgyphynance.files.wordpress.com/2008/06/final.pdf

    Rod Carvalho

    March 30, 2010 at 12:33 am

  3. Thanks Rod, I’ve added the references.

    mkz

    March 30, 2010 at 3:13 pm

  4. The link to Eric’s thesis is incorrect. The correct one is the one on my 2nd comment.

    Rod Carvalho

    March 30, 2010 at 4:18 pm

  5. I actually opened his thesis and then added the link, but still managed to add the wrong link, apparently. Thanks.

    mkz

    March 30, 2010 at 4:59 pm

  6. This is a great post. I’m sure I’ll find the links very useful in my own research. Thanks!

    David Horgan

    August 12, 2013 at 7:16 pm


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