The paper is devoted to mathematical modeling of rectangular dielectric waveguides with local periodic and fractal insets. A three-dimensional scalar boundary-value problem for the Helmholtz equation is considered. The solution is obtained numerically by means of incomplete Galerkin method and finite-difference techniques. The transmission spectra for one-, two- and three-dimensional periodic and fractal insets are computed and compared with each other. Practical applications are suggested.
Department of Mathematics, Faculty of Physics, Moscow State University, Moscow, 119991, Russia
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