| Summary: | 碩士 === 國立臺灣海洋大學 === 河海工程學系 === 94 === In the middle of 1960’s, the elliptical waveguide problem has been analyzed by means of the point-matching method. After that, many authors dealt with the same problem by various methods. In 1995, the high precision cutoff wavelengths were obtained from Zhang and Shen through calculating the modified Mathieu functions. Their solution rapidly became the benchmark for the related research topics. However, the modified Mathieu functions are very complicated special function. So, a very simple method, the boundary collocation method, is employed to investigate the elliptical waveguide with Dirichlet and Neumann boundary conditions. The effects of arrangements for the equidistant, equiangular and curvature-dependent collocation points on the precision of cutoff wave numbers are considered. Afterward the case for the superelliptical waveguide is examined extendedly. In solution procedure, the representation of the potential function is expressed firstly by separation of variables. Thus, the cutoff wave numbers and corresponding modes can be obtained by the boundary collocation method. To confirm the correctness and reliability of calculated results for elliptical and superelliptical waveguides, they are compared with Zhang and Shen’s solution and the boundary element method, respectively. According to the numerical results, it is shown that the presented results of the elliptical waveguide for eccentricity are exactly matching with those of Zhang and Shen. And the precision of the lowest 100 cutoff wavelengths can achieve 8 digits after the decimal point; no matter the equidistant, equiangular or curvature-dependent collocation points are used.
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