Discrete Electromagnetics: Maxwell's Equations Tailored to Numerical Simulations

The Finite Integration Technique (FIT) rewrites Maxwell's equations in their integral form into a discrete formulation. The resulting algebraic set of equations, the Maxwell-GridEquations (MGE), are well-suited for numerical simulation, but they represent also the theoretical basis of a discrete electromagnetic field theory. The approximation of the method lies in the construction principle of the constitutive material equations. Extensions to the socalled classical FIT such as the Non-orthogonal FIT or the Conformal FIT are presented. In addition, the basic algebraic properties of this discrete electromagnetic field theory allow to prove conservation properties with respect to energy and charge of the discrete formulation and give an explanation of the stability properties of numerical time domain formulations. The usual restriction of the FIT to a mere spatial semi-discretization scheme is explained in response to the article of Tonti [19].

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