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., $1000 × 1000$ cells giving 106 unknowns with a full 106 × 106 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.
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