Some realizations of a discrete Hodge operator: a reinterpretation of finite element techniques [for EM field analysis]

In this paper, some structures which underlie the numerical treatment of second-order boundary value problems are studied using magnetostatics as an example. The authors show that the construction of a discrete Hodge is a central problem. In this light, they interpret finite element techniques as a realization of the discrete Hodge operator in the Whitney complex. This enables one to view the Galerkin method as a way to set up circuit equations, the metric of space being encoded in the values of branch impedances