Numerical solutions of low-frequency electromagnetic problems are not a simple task, due to the inherent nature of their electrically small structures. The wavelength is very small relative to the size of the objects considered in these problems. Therefore, extremely fine meshes have to be used in the numerical solutions to perform accurate geometrical modeling of the scatterers and/or antennas. This requires extremely small unit time steps to preserve the stability of time-domain methods such as FDTD. As a result, a huge number of time iterations are required, leading to long and unacceptable computation times for today’s computer technology. Although different modifications of the FDTD algorithms have been proposed to overcome this limitation, additional speed-up techniques are needed to further reduce the computation times. The two-equations two-unknowns (2E-2U) method is a good candidate for this purpose. In this study, error analyses of the 2E-2U method for low-frequency FDTD solutions are performed in detail, and an illustrative three-dimensional scattering problem of a dielectric sphere is solved for this purpose. Critical cases for the efficient application of the 2E-2U method are clearly revealed, and some important topics are highlighted.

低频电磁问题的数值解法并非易事，这是因为它们的电结构很小。相对于这些问题中考虑的物体的尺寸，波长非常小。因此，在数值解中必须使用极细的网格，以对散射体和/或天线进行精确的几何建模。这需要极小的单位时间步长，以保持时域方法（如FDTD）的稳定性。结果，需要大量的时间迭代，导致当今计算机技术的计算时间过长且令人无法接受。尽管已经提出了FDTD算法的不同修改来克服此限制，但仍需要其他加速技术来进一步减少计算时间。为此，采用两个方程式的两个未知数（2E-2U）方法是不错的选择。在这项研究中，针对低频FDTD解决方案的2E-2U方法进行了详细的误差分析，并为此目的解决了一个说明性的介电球三维散射问题。明确揭示了有效应用2E-2U方法的关键情况，并突出了一些重要主题。