| Summary: | 碩士 === 國立海洋大學 === 河海工程學系 === 90 === In this study, the domain decomposition method and eigenfunction expansion method are employed to solve the Helmholtz eigenvalue problem for a rectangular region with line constrains. We divide the original region into several small regions along the line constrain, then we build the analytical solution and the semi-analytical solution of this problem with Dirichlet and Neumann boundary conditions. The solutions for three types of the line constrain are discussed in this study. Three types of line constrain are single line constrain, double line constrain, and inner line constrain. The analytical solution, the semi-analytical solution and the result obtained by finite element method are also compared to each other in numerical cases. The accurate results for the Helmholtz eigenvalue problem for a rectangular region with line constrains are provided in this study, they can be used to check the accuracy of the results obtained by other numerical methods.
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