This manuscript presents a fast direct solution technique for solving two dimensional wave scattering problems from quasi-periodic multilayered structures. When the interface geometries are complex, the dominant term in the computational cost of creating the direct solver scales O ( NI ) where N is the number of discretization points on each interface and I is the number of interfaces. The bulk of the precomputation can be re-used for any choice of incident wave. As a result, the direct solver can solve over 200 scattering problems involving an eleven layer geometry with complex interfaces 100 times faster than building a new fast direct solver from scratch for each new set of boundary data. An added benefit of the presented solver is that building an updated solver for a new geometry involving a replaced interface or a change in material property in one layer is inexpensive compared to building a new fast direct solver from scratch.

中文翻译：

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二维准周期多层介质散射问题的快速直接求解器

这份手稿提出了一种快速直接求解技术，用于解决准周期性多层结构的二维波散射问题。当界面几何形状复杂时，创建直接求解器的计算成本中的主要项为 O ( NI )，其中 N 是每个界面上的离散点数，I 是界面数。大量的预计算可以重新用于任何选择的入射波。因此，直接求解器可以解决 200 多个涉及具有复杂界面的 11 层几何的散射问题，比为每组新边界数据从头开始构建新的快速直接求解器快 100 倍。