电磁场时域解的差分-谱混合方法

经典的时域有限差分方法由于受到稳定性条件限制,在分析含有细微结构的散射体时,计算代价很高。为克服这一缺陷,提出了一种求电磁问题时域解的差分-谱混合方法。文中采用适当近似,将Maxwell方程中各物理量作周期延拓,利用延拓前后各物理量在第一个周期上保持不变,其频谱由连续谱变为离散谱的特性,将连续谱问题转化为离散谱求解。周期延拓后,空间各点场量的离散谱通过求解频域Maxwell差分方程得到,利用Fourier逆变换导出原问题的时域解。该方法的优点是不受稳定性条件的限制,对处理散射体特征结构尺寸远小于激励源波长的电磁问题明显优于FDTD方法,而且它能处理任何线性色散介质,和完全匹配层边界条件结合使用时不需要额外代码。数值试验表明,该方法实现简单,精度高。

A Difference-Spectrum Hybrid Method for the Solution of Maxwell Equations in Time Domain

A novel difference-spectrum hybrid numerical technique is proposed in this paper. In this method, each time dependent variable in Maxwell's equations is periodically continued with proper approximation, which results in the conversion of the continuous-spectrum problem to a discrete one by virtue of the consistent of solution before and after periodical continuation in the first period. The discrete spectra of the field quantities after continuation are obtained from difference Maxwell curl equations in frequency-domain and the time-domain solution of the original problem is derived from their inverse Fourier transforms. The strong point of the proposed method is its high capability of calculating any dispersive media and utilizing PML boundary condition without additional codes. Due to its unconditional stability, this technique excels Yee's FDTD in dealing with electromagnetic problems where the characteristic sizes of the scatter are much larger than the wavelength of the stimulant source. Numerical experiments demonstrate its effectiveness, easy implementation and high precision.