| Summary: | 碩士 === 國立海洋大學 === 河海工程學系 === 91 === In this thesis, boundary integral equations and boundary element methods were
employed semi-analytically and numerically to study on the occurrence of both the
spurious eigenvalues and fictitious frequencies for the interior and exterior Helmholtz equations
with the mixed-type boundary conditions, respectively. For the interior acoustic problem, the
degenerate kernels of fundamental function and Fourier series were utilized for null-field equation
to derive the true and spurious eigenfunctions analytically. The complex-valued BEM,
the real-part BEM, the imaginary-part BEM and the MRM were utilized to solve the
eigenproblem and eigenmodes. The results are compared with FEM. Moreover, the SVD
updating techniques in conjunction with the Fredholm''s alternative theorem
were adapted to sort out the spurious eigenvalues and extract out the true ones. For the
exterior radiation problem, the same mathematical tools were utilized to derive the
field solution analytically. The complex-valued BEM was utilized to
solve the fictitious frequencies in the exterior acoustic problem.
The CHIEF and Burton \& Miller methods were adopted to suppress the occurrence
of the fictitious frequencies. It is emphasized that the
occurrence of not only spurious eigenvalues but also fictitious frequencies
depend on the adopted method (singular or hypersingular formulation)
no matter what the given types of boundary conditions for the problem are.
The illustrative examples were verified successfully.
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