  We look at computational physics from an electrical engineering perspective
and suggest that several concepts of mathematics, not so well-established in
computational physics literature, present themselves as opportunities in the
field. We discuss elliptic complexes and highlight the category theoretical
background and its role as a unifying language between algebraic topology,
differential geometry, and modelling software design. In particular, the
ubiquitous concept of naturality is central. Natural differential operators
have functorial analogues on the cochains of triangulated manifolds. In order
to establish this correspondence, we derive formulas involving simplices and
barycentric coordinates, defining discrete vector fields and a discrete Lie
derivative as a result of a discrete analogue of Cartan's magic formula. This
theorem is the main mathematical result of the paper.
