We present a recursive version of the previously proposed fast algorithm for computation of the field scattered from arbitrary-shaped multilayer objects. As in the original version, the field at each layer is represented by a series of cylindrical functions with unknown coefficients. In order to determine these coefficients, a linear system of equations is obtained through a procedure based on the boundary conditions between the layers. Instead of solving this large system by applying conventional linear solvers as done in the original version, through an approach based on Thomas algorithm, we derive recursive expressions to compute the scattered field. While the accuracy of the results for both versions are almost the same, the recursive version has lower time and memory complexity. Hence, it supersedes the original version.

中文翻译：

---

任意形状多层圆柱体电磁散射的有效递归方法

我们提出了先前提出的快速算法的递归版本，用于计算从任意形状的多层物体散射的场。与原始版本一样，每一层的场由一系列未知系数的圆柱函数表示。为了确定这些系数，通过基于层间边界条件的程序获得线性方程组。我们不是像原始版本那样通过应用传统的线性求解器来求解这个大型系统，而是通过基于 Thomas 算法的方法，推导出递归表达式来计算散射场。虽然两个版本的结果准确性几乎相同，但递归版本的时间和内存复杂度较低。因此，它取代了原始版本。