The finite-difference time-domain (FDTD) method is a widely used numerical technique for simulating electromagnetic wave interactions with complex media. Various efficient approaches have been used to analyze complex media, and the surface impedance boundary condition (SIBC) is one of the most powerful techniques in FDTD simulations, allowing efficient electromagnetic modeling of lossy materials. However, conventional SIBC-FDTD formulations face challenges when analyzing lossy dispersive materials because of the assumption of frequency-independent relative permittivity and conductivity in the inverse Laplace transform. To address this, we propose a dispersion-modeling approach for the surface impedance of lossy dispersive materials. Additionally, to reduce grid errors in the FDTD discrete domain, we introduce the surface admittance boundary condition (SABC) for lossy dispersive materials. We investigated the numerical accuracy by deriving the numerical surface impedance and admittance for the proposed surface boundary condition (SBC)-FDTD formulations. In addition, we determined the numerical stability conditions of the SBC-FDTD formulations using the von Neumann method combined with the Routh-Hurwitz criterion. Numerical examples validate both the numerical accuracy and stability of the proposed SBC-FDTD formulations. Our findings enhance the understanding and application of the SBC in FDTD simulations, especially for lossy dispersive materials, and provide insights for future research and electromagnetic modeling in various fields.

中文翻译：

---

有损色散介质的基于表面边界条件 (SBC) 的 FDTD 公式


时域有限差分 (FDTD) 方法是一种广泛使用的数值技术，用于模拟电磁波与复杂介质的相互作用。各种有效的方法已用于分析复杂介质，表面阻抗边界条件 (SIBC) 是 FDTD 仿真中最强大的技术之一，可以对有损材料进行有效的电磁建模。然而，由于拉普拉斯逆变换中假设频率无关的相对介电常数和电导率，传统的 SIBC-FDTD 公式在分析有损色散材料时面临挑战。为了解决这个问题，我们提出了一种用于有损色散材料表面阻抗的色散建模方法。此外，为了减少 FDTD 离散域中的网格误差，我们引入了有损色散材料的表面导纳边界条件 (SABC)。我们通过推导所提出的表面边界条件 (SBC)-FDTD 公式的数值表面阻抗和导纳来研究数值精度。此外，我们使用冯·诺依曼方法结合劳斯-赫尔维茨准则确定了 SBC-FDTD 公式的数值稳定性条件。数值例子验证了所提出的 SBC-FDTD 公式的数值准确性和稳定性。我们的研究结果增强了 SBC 在 FDTD 模拟中的理解和应用，特别是对于有损色散材料，并为各个领域的未来研究和电磁建模提供了见解。