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Progress In Electromagnetics Research
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ELECTROMAGNETIC THEORY WITH DISCRETE EXTERIOR CALCULUS

By S. C. Chen and W. C. Chew

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Abstract:
A self-contained electromagnetic theory is developed on a simplicial lattice. Instead of dealing with vectorial field, discrete exterior calculus (DEC) studies the discrete diff erential forms of electric and magnetic fields, and circumcenter dual is adopted to achieve diagonal Hodge star operators. In this paper, Gauss' theorem and Stokes' theorem are shown to be satisfi ed inherently within DEC. Many other electromagnetic theorems, such as Huygens' principle, reciprocity theorem, and Poynting's theorem, can also be derived on this simplicial lattice consistently with an appropriate defi nition of wedge product between cochains. The preservation of these theorems guarantees that this treatment of Maxwell's equations will not lead to spurious solutions.

Citation:
S. C. Chen and W. C. Chew, "Electromagnetic Theory with Discrete Exterior Calculus," Progress In Electromagnetics Research, Vol. 159, 59-78, 2017.
doi:10.2528/PIER17051501
http://www.jpier.org/PIER/pier.php?paper=17051501

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