Simulating electromagnetic fields across broad frequency ranges is challenging due to numerical instabilities at low frequencies. This work extends a stabilized two-step formulation of Maxwell's equations to the time-domain. Using a Galerkin discretization in space, we apply two different time-discretization schemes that are tailored to the first- and second-order in time partial differential equations of the two-step solution procedure used here. To address the low-frequency instability, we incorporate a generalized tree-cotree gauge that removes the singularity of the curl-curl operator, ensuring robustness even in the static limit. Numerical results on academic and application-oriented 3D problems confirm stability, accuracy, and the method's applicability to nonlinear, temperature-dependent materials.

翻译：在宽频范围内模拟电磁场具有挑战性，因为低频时会出现数值不稳定性。本研究将麦克斯韦方程组的稳定化两步公式扩展到时域。通过空间上的伽辽金离散化，我们采用了两种不同的时间离散化方案，这两种方案分别针对此处所用两步求解程序中时间上一阶和二阶的偏微分方程而定制。为解决低频不稳定性，我们引入了一种广义的树-余树规范，以消除旋度-旋度算子的奇异性，从而确保即使在静态极限下也具有鲁棒性。在学术和应用导向的三维问题上的数值结果证实了该方法的稳定性、准确性以及对非线性、温度依赖性材料的适用性。