| Summary: | 博士 === 國立海洋大學 === 河海工程學系 === 91 === In this dissertation, we employ the dual BEM to solve the acoustics and the propagation of oblique incident wave passing a thin barrier with rigid, absorbing and porous boundary conditions. A detailed mathematical derivations for obtaining all the improper integrals of the four kernel functions ($UT$ in the singular equation, $LM$ in the hypersingular equation) in the dual integral equations are studied. The roles of hypersingular integral equation in the dual BEM for the problems are addressed, and a dual BEM program is developed to solve the problems. To enhance the efficiency in numerical computation of the dual BEM, we adopt two techniques to accelerate the rate of convergence. Firstly, we develop
adaptive BEM scheme for propagating solutions of the acoustics
and water wave problems in the dual BEM. Two kinds of error
indicators obtained from the dual integral equations are constructed for the local error estimation, which are the essential ingredients for all adaptive mesh schemes in the BEM. The two error tracking curves can decide where the elements need to be refined. Secondly, we adopt the concept of
Fast Multipole expansion Method (FMM) to accelerate the computation rate of influence matrix in the dual BEM.
We solve the large scale problems of the exterior acoustics and oblique incident water wave passing a submerged barrier by using the improved DBEM. By adopting the addition theorem,
the four kernels for the Helmholtz equation and the modified Helmholtz equation are expanded into degenerate kernels which can separate the field point and source point. The separable technique can promote the efficiency in determining the influence coefficients in a similar way of Fast Fourier Transform (FFT) over Fourier Transform (FT). To accelerate the convergence rate in constructing the influence matrix, the center of multipole is designed to locate on the center of local coordinate for each boundary element. The singular and hypersingular integrals are transformed into the summability of divergent series and regular integrals. Furthermore,
We develop four meshless methods based on the potential theory using the radial basis function for solving the exterior acoustic problems. Both the null-field approach and the method of fundamental solution (MFS) are utilized.
We can determine the diagonal term of influence matrices using the radial basis functions free of the singularity and boundary integrals. Finally,
the results of several examples are compared with those of FEM, experiment and analytical solution using eigenfunction expansion.
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