Abstract A new 3D unsplit Godunov scheme for solving Maxwell’s equations with polarization is presented. The numerical scheme avoids the use of limiters by interpolating the field components that are continuous at cell boundaries, making the algorithm simpler and faster. The algorithm allows the use of metals and a wide variety of polarization models: Lorentz, non-linear as Kerr type or Havriliak–Negami dielectric model. Moreover, the algorithm can use Adaptive Mesh Refinement (AMR) to simulate systems with sharp steps in material properties as well as the propagation of short-wavelength pulses in great domains with a reasonable computational effort. With AMR the resulting method is faster in computer time compared to FDTD at the same accuracy. Furthermore, a divergence control algorithm has been implemented, although it is not needed in all the tests performed so far.

中文翻译：

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EMcLAW：麦克斯韦方程的未分裂 Godunov 方法，包括极化、金属、发散控制和 AMR

摘要 提出了一种求解麦克斯韦极化方程的新的3D不分裂Godunov格式。数值方案通过内插在单元边界处连续的场分量来避免使用限制器，从而使算法更简单、更快。该算法允许使用金属和多种极化模型：洛伦兹、非线性 Kerr 类型或 Havriliak-Negami 介电模型。此外，该算法可以使用自适应网格细化 (AMR) 来模拟在材料特性方面具有急剧变化的系统，以及以合理的计算工作量在大域中传播短波长脉冲的系统。在相同精度下，与 FDTD 相比，使用 AMR 所得方法在计算机时间上更快。此外，还实施了发散控制算法，