The full-wave simulation of complex electromagnetic (EM) surfaces, such as reflectarrays and metasurfaces, is a challenging problem. In this article, we present a macromodeling approach to efficiently simulate complex EM surfaces composed of PEC traces, possibly with fine features, on a finite-sized multilayer dielectric substrate. In our approach, we enclose each element of the structure with a fictitious surface. By applying the equivalence principle on each surface, we derive a macromodel for each element of the array. This macromodel consists of a linear operator that relates the equivalent electric and magnetic current densities introduced on the fictitious surface. Mutual coupling between the elements of the structure is captured by the equivalent current densities in a fully accurate way. The crux of the proposed technique is to solve for equivalent current densities on the fictitious surface instead of directly solving for the actual current densities on the original scatterer. When simulating complex surfaces, this approach leads to fewer unknowns and better conditioning. We also propose a rigorous acceleration algorithm based on the fast Fourier transform to simulate electrically large surfaces. Numerical results demonstrate that the proposed approach is significantly faster and requires less memory than commercial solvers based on the surface integral equation method while giving accurate results.

中文翻译：

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一种有效模拟非均匀电磁表面的快速宏观建模方法

复杂电磁 (EM) 表面（例如反射阵列和超表面）的全波仿真是一个具有挑战性的问题。在本文中，我们提出了一种宏观建模方法，可在有限尺寸的多层介电基板上有效地模拟由 PEC 迹线组成的复杂 EM 表面，可能具有精细特征。在我们的方法中，我们用一个虚构的表面包围了结构的每个元素。通过在每个表面上应用等效原理，我们为阵列的每个元素推导出一个宏模型。该宏模型由一个线性算子组成，该算子关联了虚拟表面上引入的等效电流和磁流密度。结构元件之间的相互耦合由等效电流密度以完全准确的方式捕获。所提出技术的关键是求解虚拟表面上的等效电流密度，而不是直接求解原始散射体上的实际电流密度。在模拟复杂表面时，这种方法会导致更少的未知数和更好的调节。我们还提出了一种基于快速傅立叶变换的严格加速算法来模拟电大表面。数值结果表明，与基于表面积分方程方法的商业求解器相比，所提出的方法明显更快，所需内存更少，同时给出准确的结果。这种方法导致更少的未知数和更好的条件。我们还提出了一种基于快速傅立叶变换的严格加速算法来模拟电大表面。数值结果表明，与基于表面积分方程方法的商业求解器相比，所提出的方法明显更快，所需内存更少，同时给出准确的结果。这种方法导致更少的未知数和更好的条件。我们还提出了一种基于快速傅立叶变换的严格加速算法来模拟电大表面。数值结果表明，与基于表面积分方程方法的商业求解器相比，所提出的方法明显更快，所需内存更少，同时给出准确的结果。