A mathematical model for a rectangular waveguide with an impedance boundary condition has been formulated and substantiated. The model is based on the application of the Galerkin boundary method. It is assumed that the surface impedance is not a constant, but is a function of the coordinates on the surface. The solution is represented as a linear combination of coordinate functions, each of which exactly satisfies Maxwell’s equations inside a cylindrical domain. The set of coordinate functions at the border forms a complete system. The coefficients are determined from the orthogonality condition for the surface residual to the system of projection functions. Because of the use of the Galerkin method, the projection functions coincide with the system of coordinate functions. To calculate the guided waves of a rectangular waveguide with an impedance boundary, a homotopy method has been proposed and justified. The decomposition of the solution into a power series in a small parameter has also been constructed.

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计算具有阻抗边界的圆柱形波导导波的同伦方法

公式化并证明了具有阻抗边界条件的矩形波导的数学模型。该模型基于Galerkin边界方法的应用。假设表面阻抗不是常数，而是表面坐标的函数。该解表示为坐标函数的线性组合，每个坐标函数都精确满足圆柱域内的麦克斯韦方程组。边界处的一组坐标函数构成一个完整的系统。系数是根据投影函数系统的表面残差的正交性条件确定的。由于使用了Galerkin方法，投影函数与坐标函数系统重合。为了计算具有阻抗边界的矩形波导的导波，提出了同伦方法并证明了其合理性。还构造了将溶液分解为小参数的幂级数的方法。