Discrete electromagnetic theory with exterior calculus
Discrete electromagnetic theory with exterior calculus
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具有外微积分的离散电磁理论
DOI：
10.1109/piers.2016.7734512
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
W. Chew
中科院分区：
文献类型：
--
作者：
Shu C. Chen;W. Chew
在简单格上建立了一个自包含的电磁理论。离散外微积分（DEC）研究电场和磁场的离散微分形式，而不是处理向量场。采用环心对偶来实现霍奇星算子的对角性和简单性。本文证明了高斯定理和斯托克斯定理是固有满足的。许多其他的电磁定理，如互易定理，可以在这个简单格上得到一致的，与形式之间的楔形积的适当定义一致。这些定理的保留保证了对麦克斯韦方程组的这种处理不会导致虚假的解。
A self-contained electromagnetic theory is developed on a simplicial lattice. Instead of dealing with vectorial field, discrete exterior calculus (DEC) studies the discrete differential forms of electric and magnetic fields. Circumcenter dual is adopted to achieve diagonality and simplicity of Hodge star operators. In this paper, Gauss' theorem and Stokes' theorem are shown to be satisfied inherently. Many other electromagnetic theorems, like reciprocity theorem, can be derived on this simplicial lattice consistently with an appropriate definition of wedge product between forms. The preservation of these theorems guarantees that this treatment of Maxwell's equations will not lead to spurious solutions.