Discrete Exterior Calculus (DEC) [8] is a discrete version of the Smooth Exterior Calculus [2]. Exterior calculus is calculus on smooth manifolds, and DEC is a calculus for discrete manifolds, the logical connection is obtained through the algebraic topology methods applied to simplicial meshes. The main application area of DEC, is the creation of discrete operators (e.g Divergence, Gradient, Curl) to be used in numerical methods for Partial Differential Equations. Important fields of application of DEC algorithms are computational mechanic [11], fluid dynamic, electromagnetism [4] and computer graphics. We describe the implementation of Discrete Exterior Derivative and Discrete Hodge Star, that act on discrete differential forms in a way that faithfully mirrors the behavior of the smooth operators [3], [9]. The implementation of this calculus requires an appropriate data structure to represent the primal mesh and its dual (circumcentric dual), because it needs to support local traversal of elements, adjacency and orientation information for the simplices of any dimension. In this paper, after a brief introduction on DEC theory, we will describe our implementation of the Discrete Exterior Derivative[8] and Discrete Hodge Star[8]. The paper end with a short description of the DEC application implement the mathematical problem of decomposition of vector field.
