In this paper, two high order complex contour discretization methods are proposed to simulate wave propagation in locally perturbed periodic closed waveguides. As is well known the problem is not always uniquely solvable due to the existence of guided modes. The limiting absorption principle is a standard way to get the unique physical solution. Both methods are based on the Floquet-Bloch transform which transforms the original problem to an equivalent family of cell problems. The first method, which is designed based on a complex contour integral of the inverse Floquet-Bloch transform, is called the CCI method. The second method, which comes from an explicit definition of the radiation condition, is called the decomposition method. Due to the local perturbation, the family of cell problems are coupled with respect to the Floquet parameter and the computational complexity becomes much larger. To this end, high order methods to discretize the complex contours are developed to have better performances. Finally we give the convergence results which we confirm with numerical examples.

翻译：在本文中,提出了两种高序复杂等离散方法,以模拟波波在局部扰动周期闭合波制导器中的传播。众所周知,由于有导引模式,问题并不总是特别容易溶解。限制吸收原则是获取独特物理解决方案的标准方法。两种方法都基于Floquet-Bloch变形法,将原始问题转化为同类的细胞问题。第一种方法,根据反面Floquet-Bloch变形的复杂轮廓组合设计,称为CCI法。第二种方法,由辐射条件的明确定义产生,称为分解法。由于本地的扰动,细胞问题与Floquet参数和计算复杂程度相结合。为此,开发了将复杂轮廓分解的高度顺序方法,以便有更好的性能。最后,我们用数字实例来证实这些趋同结果。