| Summary: | 碩士 === 國立臺灣海洋大學 === 河海工程學系 === 93 === The main purpose of this thesis is to study the triangular and quadrilateral waveguides. The eigenvalue problems with Dirichlet and Neumann boundary conditions are solved by applying the boundary collocation and region-matching method, and the shapes of waveguides in this study are right triangle, obtuse triangle, parallelogram and trapezoid. Furthermore, concerning about the effects of the position of collocation points which places on different undetermined boundary in the computational domain, the convergence of cut-off wavenumbers for these shapes in present is discussed. Following the solution procedure of the boundary collocation method, the expression of the potential function for the whole computational domain is obtained firstly. Placing the collocation points on the boundary and the boundary conditions are employed to construct the simultaneous equations for the problem, then the cut-off wavenumbers can be gained. As regards the solution procedure of region-matching method, an auxiliary boundary is introduced to divide the whole computational domain into two sub-regions. And in each region, the expression of the potential function for one is derived. Afterward, the local coordinate systems of each sub-region are unified by utilizing the coordinate transformation formulas. Finally, the collocation method and continuity conditions at the boundary between adjacent regions are applied to determine the cut-off wavenumbers from a linear algebra equation set. To verify the correctness and reliability of computational results in this thesis, all of them are compared with those of the boundary element method (BEM). It shows that the presented results and those of BEM are in good agreement with each other. When using the boundary collocation method which places the collocation points on different side of the triangular region to determine the cut-off wavenumbers, the convergence for placing points on the short side of a right triangle would be better than other sides. Furthermore, when applying the region-matching method which places the collocation points on different diagonal of the quadrilateral region to determine the cut-off wavenumbers, the convergence for placing points on the long diagonal of a quadrilateral would be better than short one.
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