| Summary: | 碩士 === 國立海洋大學 === 河海工程學系 === 88 === For the potential or plane elasticity problem, the special geometry dimension which results in a nonunique solution is called
degenerate scale. In the thesis, the problem of the degenerate scale in BEM is analytically and numerically studied. For the
potential problem, the occurrence of the degenerate scale depends on the outer boundary. For the plane elasticity problem, it
depends on not only outer boundary but also on the Poisson''s ratio. The hypersingular formulation fails in solving the
multiply-connected domain problem. Singular value decomposition technique is used to determine the positions of the degenerate
scale numerically by examining the minimum singular value. We can deal with the degenerate scale problem and obtain the accurate solution by adding a constant in the
fundamental solution.
In order to solve the
multiply-connected domain problem using hypersingular formulation, we obtain the acceptable results by employing pseudo-inverse technique.
For the acoustic problem, the complex-valued kernel function was employed to solve the natural frequency traditionally. However, to
avoid complicated computation, only the real-part or imaginary-part is used, which thus results in spurious eigensolutions. For the
multiply-connected acoustic problem, even though the complex-valued kernel is used, the spurious eigenvalues still occur. In
the thesis, the mechanism of the spurious eigenvalues is studied mathematically. Burton and Miller method is used to filter
out the spurious eigenvalues. Also, a more efficient method is proposed to eliminate the spurious eigenvalues by choosing only real-part kernel in the Burton and Miller method. Numerical examples
are demonstrated to show the validity of the proposed method.
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