Discrete differential forms for computational modeling
The emergence of computers as an essential tool in scientific research has shaken the very foundations of differential modeling. Indeed, the deeply-rooted abstraction of smoothness, or differentiability, seems to inherently clash with a computer's ability of storing only finite sets of numbers. While there has been a series of computational techniques that proposed discretizations of differential equations, the geometric structures they are supposed to simulate are often lost in the process.
© 2005 ACM. The authors wish to first thank Jerrold E. Marsden for his tremendous help and support along the way. We also wish to acknowledge the support of Anil Hirani, Melvin Leok, David Cohen-Steiner, Peter Schrőder, Sharif Elcott, Pierre Alliez, and Eitan Grinspun.