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Progress In Electromagnetics Research
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'GENERALIZED FINITE DIFFERENCES' IN COMPUTATIONAL ELECTROMAGNETICS

By A. Bossavit

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Abstract:
The geometrical approach to Maxwell's equations promotes a way to discretize them that can be dubbed "Generalized Finite Differences", which has been realized independently in several computing codes. The main features of this method are the use of two grids in duality, the "metric-free" formulation of the main equations (Amp`ere and Faraday), and the concentration of metric information in the discrete representation of the Hodge operator. The specific role that finite elements have to play in such an approach is emphasized, and a rationale for Whitney forms is proposed, showing why they are the finite elements of choice.

Citation: (See works that cites this article)
A. Bossavit, "'Generalized Finite Differences' in Computational Electromagnetics," Progress In Electromagnetics Research, Vol. 32, 45-64, 2001.
doi:10.2528/PIER00080102
http://www.jpier.org/PIER/pier.php?paper=00080102

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