| Summary: | 碩士 === 國立海洋大學 === 系統工程暨造船學系 === 88 === In this thesis, the eigenvalue problem of the Helmholtz equation is solved by using the Fictitious Boundary Element Method which is generally categorized into the General Indirect Method with regular formulation. In the numerical implementations, there may exist spurious eigenvalues and numerical contamination phenomena, the General Singular Value Decomposition Method in conjunction with a linear homogeneous auxiliary boundary system, which is independent of the original one, are thus proposed to solve the problem. It is proved that both the original and auxiliary systems will result in the spurious eigenvalue and the proposed approach can effectively solve the spurious eigenvalues and numerical contamination at the same time. For the numerical validation, the characteristics of circulant in the coefficient matrix for the circular problem and the seldom used Trefftz method in the interior dynamic problem are adopted for comparisons. Moreover, the numerical examples illustrated here put an emphasis on the generalization of the Fictitious Boundary Element Method. Finally, the results show that the proposed approach can not only describe the responses in the interior field points by using the original equation but also solve the multi-connected problems by adding the extra solution basis.
|
|---|
