We consider the problem of diffraction of a waveguide wave by an impedance rod in a rectangular waveguide with perfectly conducting walls and the problem of diffraction of a plane two-dimensional electromagnetic wave and the field of a point source by an evenly spaced array formed by infinite cylinders of arbitrary cross-section with perfectly and well conducting walls. Both problems are reduced to solving contour Fredholm integral equations. Such reduction is based on using the Green’s function of an empty planar waveguide and a quasiperiodic Green’s function, which are infinite series in the eigenfunctions of the cross-section of the planar waveguide and in the eigenfunctions satisfying the Floquet conditions. To calculate the kernels of the resulting integral equations, depending on both the Green’s functions themselves and their derivatives, we have developed special algorithms to improve the convergence of the series and explicitly isolate the logarithmic singularity occurring in the series.

中文翻译：

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波导和周期结构中波衍射问题积分方程的核研究

我们考虑了具有完美导电壁的矩形波导中阻抗棒对波导波的衍射问题，以及平面二维电磁波和点源场由无穷大构成的均匀间隔阵列的衍射问题。具有完美导电壁的任意截面圆柱体。这两个问题都简化为求解轮廓 Fredholm 积分方程。这种减少基于使用空平面波导的格林函数和准周期格林函数，它们是平面波导横截面的本征函数和满足 Floquet 条件的本征函数的无穷级数。要计算所得积分方程的核，取决于格林函数本身及其导数，