We studied the harmonic magnetodynamic behavior (without free space wave propagation) of a resonant surface metamaterial, made of many identical and regularly arranged LC cells. The circuit model gives the exact solution, but it is not numerically efficient for simulating very large structures (e.g., $1000 \times 1000$ cells giving 10⁶ unknowns with a full $10^{6} \times 10^{6}$ matrix). For the first time, we highlight the modal characteristics of the spatial solutions, which make it possible to explain their frequency- and spatial-related properties. From these results, we show under what assumptions it is possible to significantly lighten the system of equations, which opens up the way to develop more efficient numerical methods.

中文翻译：

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大表面 LC 共振超材料：从电路模型到模态理论和有效的数值方法

我们研究了由许多相同且规则排列的谐振表面超材料的谐波磁动力学行为（没有自由空间波传播） 液晶显示器细胞。电路模型给出了精确的解决方案，但对于模拟非常大的结构（例如， 1000 美元\乘以 1000 美元 单元格给出 10 ^{6 个}未知数 $10^{6} \times 10^{6}$ 矩阵）。我们第一次强调了空间解的模态特征，这使得解释它们的频率和空间相关属性成为可能。从这些结果中，我们展示了在哪些假设下可以显着简化方程组，这为开发更有效的数值方法开辟了道路。