Application of the boundary‐element method to an infinitely long tunnel

Abstract

AbstractA hollow waveguide or a tunnel made of a lossy dielectric material such as concrete is presumed. A method of analyzing the wave propagation inside the tunnel by the boundary‐element method is formulated. When the boundary‐element method is applied to an infinitely long tunnel or a tunnel containing a bend or a branch, it is necessary to truncate the tunnel at a finite length. In addition, an analytical matching condition similar to the one for a lossless metal waveguide must be provided at the fictitious boundary. In this paper, a tunnel with a surface impedance approximation as the boundary condition on the lossy dielectric wall (so‐called impedance tunnel) is considered. First, an analytical solution is derived for a uniform impedance tunnel. Next, a method is proposed in which the analytical solution and the boundary‐element method are coupled on the forementioned hypothetical boundary. The algorithm is described in detail. For a straight tunnel, it is confirmed that the results agree well with those by the Fourier integral even when the imaginary part of the relative permittivity is small. Problems of finding electromagnetic fields inside a semi‐infinite tunnel excited by a line current source or an infinitely long tunnel with an aperture are studied. It is pointed out that the present method is extremely useful for a hollow waveguide consisting of a lossy dielectric medium such as concrete. The difference from the case of a lossless metal waveguide is investigated.