Finite Integration Method and Discrete Electromagnetism

We review some basic properties of the Finite Integration Technique (FIT), a generalized finite difference scheme for the solution of Maxwell’s equations. Special emphasis is put on its relations to the Finite Difference Time Domain (FDTD) method, as both algorithms are found to be computationally equivalent for the special case of an explicit time-stepping scheme with Cartesian grids. The more general discretization approach of the FIT, however, inherently includes an elegant matrix-vector notation, which enables the application of powerful tools for the analysis of consistency, stability, and other issues. On the implementation side this leads to many important consequences concerning the basic method as well as all kinds of extensions.

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