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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.
In order to solve the problem that the finite difference method in time domain has large error in the existing conformal technique of the metamaterial cell and the parallel direction is not included, a new algorithm for calculating the cross-cell cellular conformality by using the electric field numerical weighting method is proposed. Instead of weight-averaged the dielectric constant ε, the proposed algorithm weights the real solution component electric field strength of the finite-difference time-domain method according to the median value theorem and multiplies the weight into the integral path. Considering the discontinuous effects of the cross-media Amperes loop cells and the cross-media Faraday loop cells on the results, we can apply various kinds of positional relationships between the media interface and the cell mid-field components, with high universality and accuracy High and easy to implement.With the medium-filled circular waveguide as a numerical model for theoretical numerical calculation and simulation verification, the eigenvalues and theoretical values of two-dimensional TE modes with different conformal methods are compared, To the dissimilarity.The numerical results show that the eigenvalue obtained by the proposed algorithm is the closest to the theoretical value and the anisotropy caused by the algorithm is smaller, When the effectiveness of the cell.