Conservation of discrete energy and related laws in the finite integration technique

Abstract

We report some properties of the Finite Integration Technique (FIT), which are related to the definition of a discrete energy quantity. Starting with the well-known identities for the operator matrices of the FIT, not only the conservation of discrete energy in time and frequency domain simulations is derived, but also some important orthogonality properties for eigenmodes in cavities and waveguides. Algebraic proofs are presented, which follow the vector-analytical proofs of the related theorems of the classical (continuous) theory. Thus, the discretization approach of the FIT can be considered as the framework for a consistent discrete electromagnetic field theory.