基于电场数值加权的跨介质元胞共形新技术

针对时域有限差分法处理跨介质元胞现有共形技术中存在误差大、平行方向未被包含等问题, 提出一种利用电场数值加权法来进行跨介质元胞共形计算的新算法. 该算法不再对介电常数ε做加权平均处理, 而是根据中值定理对时域有限差分法真正的求解分量电场强度进行权值选择, 并将权值乘入积分路径中. 该方法同时考虑了跨介质安培环路元胞与跨介质法拉第环路元胞对结果带来的不连续影响, 而且对介质界面与元胞中场分量的各种位置关系均能应用, 通用性强、精度高且易于实现. 利用介质填充圆波导作为数值模型来进行理论数值计算和仿真验证, 比较不同共形方法的二维TE模式的特征根与理论值的偏差以及由共形技术所带来的各向相异性. 数值结果表明, 本文所提出算法求得的特征根最接近理论值, 而且造成的各向相异性更小, 从而验证了该算法在处理跨介质元胞时的有效性.关键词：时域有限差分电场数值加权法二维TE模式跨介质元胞

A new conformal technique of inhomogeneous cells based on electric field strength weighted values*

In this paper, a new method of using the electric field numerical weight to process the inhomogeneous cells is proposed, which is to resolve the problems such as high errors and parallel direction excluded in the existing finite-difference time-domain method. Instead of deriving average dielectric constant, the new method weights the electric field strength, which is the true solving variables, according to the mean value theorem, and then the length of the integral path is multiplied by the weight. In the new method both the discontinuous effects of inhomogeneous Ampere cell and the ones of inhomogeneous Faraday cell are taken into account, so it is accurate, easy to implement, versatile, and applicable to any of the various positional relationships between the dielectric interface and the electric field strength variable. A numerical model of dielectric filled circular waveguide is used for the numerical calculation and simulation, in which the deviations of the characteristic roots in two-dimensional TE mode solved by different methods from the theoretical ones are compared, and the anisotropies of different methods are also compared. The numerical result shows that the characteristic roots solved by the presented method are closer to the theoretical ones and the anisotropy caused by the proposing method is lower, which proves that this method is more efficient to process the inhomogeneous cells.
Keywords：finite-difference time-domainelectric field numerical weighting methodtwo-dimensional TE modeinhomogeneous cell