A Multivector Data Structure for Differential Forms and Equations

Abstract

We propose a combinatorial data structure for representing multivectors [2, 3] in an n-dimensional space. The data structure is organized around a collection of abstract K-dimensional cells, k = 0,1,...,n that are assembled into an oriented cellular structure called a starplex and shown in Figure 11.1. The starplex structure represents the combinatorial neighborhood (a star) of a 0-cell in any n-dimensional cell complex representing a typical coordinate control element (usually cubical or simplicial). The combinatorics of the starplex matches exactly the combinatorial structure of the multivector: every oriented k-cell in the starplex corresponds to some basis K-vector.