Geometric Aspects of the Simplicial Discretization of Maxwell's Equations- Abstract

Abstract

Aspects of the geometric discretization of electromagnetic fields are considered. The convenience of the use of differential forms to represent the field quantities through natural role as duals (cochains) of the geometric constituents of the lattice (nodes, edges, faces, volumes) is reviewed. The use of a (primary) simplicial lattice, and a barycenter subdivision to decompose the associated (barycentric) dual lattice into simplicial elements are treated briefly. Using this subdivision, lattice Hodge operators are built by defining Whitney maps on the barycentric subdivision.