标题： 一种稳定的时间域麦克斯韦方程组的两步公式 显示英文标题

标题： A stabilized Two-Step Formulation of Maxwell's Equations in the time-domain

摘要： 在宽频范围内模拟电磁场由于低频下的数值不稳定性而具有挑战性。 这项工作将麦克斯韦方程组的稳定两步公式扩展到时域。 使用空间中的伽辽金离散化，我们应用了两种不同的时间离散化方案，这些方案专门针对此处使用的两步求解过程中的第一和第二阶时间偏微分方程。 为了解决低频不稳定性问题，我们引入了一个广义的树-余树规范，该规范消除了旋度-旋度算子的奇异性，确保在静态极限下仍具有鲁棒性。 学术性和应用性三维问题的数值结果证实了该方法的稳定性、准确性以及其对非线性、温度相关材料的适用性。 显示英文摘要

摘要： 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.