[2] In solving of many practical problems concerning electromagnetic field propagation one has to deal with cases of the presence of singular points (sharp edge, corners, etc.) at the boundary of the propagation region. Modeling of the problem of radio wave propagation in the Earth-ionosphere waveguide is one of such problems. One of the main aims in this problem is to take into account irregularities which may exist at the lower wall (the Earth) and especially of angular points (mountain ridges, electric power lines) which lead to appearance of peculiarities in the fields. The ionospheric disturbances are smooth or absent. As far as the main attention is paid to the role of irregularities, the walls of the model waveguide are chosen to be conducting ideally.
[3] The presence of angular points at the boundary of the propagation region even in the simplest cases complicates considerably numerical solution of the problem: the equation systems obtained by the simple joining method have unlimited in l2 operators, whereas the truncation method has in the best case a conventional (i.e., dependent of the truncation method) convergence [Mittra and Li, 1974]. So solving such problems one should use some regularization methods. The main methods of solving such problems are: the method of inversion of the residuals of part of the matrix operator [Shestopalov et al., 1973] the method of residues [Mittra and Li, 1974], the method of quasi-static Green function (MQGF) [Verbitsky, 1981], and also the semi-inversion method (SIM) [Maison and Makarov, 1996], the latter two methods being used in this paper.
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