Title: Discrete exterior calculus with convergence to the smooth continuum 

Speaker: Jenny Harrison, Univ. of Calif., Berkeley

Date/Time: Thursday, August 11, 2005, 10:00-11:00 am

Location: Building 980, Room 95 (Sandia NM)

Brief Abstract: By articulating the concept of an infinitesimal within the framework of classical analysis, we may define integral and derivative at a single point in space. Theorems of Stokes and Gauss can be stated and proved at a single point. The theory extends immediately to a discrete theory by taking sums over finitely many points in space.   Convergence to the smooth continuum is satisfied, leading readily to a full theory of calculus beyond the classical setting, including calculus on fractals and soap films.

The discrete theory has well behaved operators and products that avoid common problems of other approaches. For example,  

1. The product on discrete forms is associative and graded commutative. 
2. Operators on domains, such as boundary and Hodge star, are geometrically defined as limits in the strong topology, not as duals to differential forms, or through meshes.
3. Forms and cochains are isomorphic
4. Convergence to the smooth continuum is guaranteed.

CSRI POC: Pavel Bochev, (505) 844-1990