Discretising geometry and preserving topology I: A discrete exterior calculus

Abstract

A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are not solely topological theories. Issues of convergence and a numerical implementation are discussed. The follow-up article covers the resulting discretisation scheme with metric data.

26 pages, improved version with Lie group interpretation. References added