| Summary: | 碩士 === 國立海洋大學 === 河海工程學系 === 87 === Based on the dual framework derived by Hong and Chen, we developed symmetric
boundary element method, instead of conventional BEM. Using the symmetry properties
for the four kernels in the dual BEM, the symmetric BE formulation can be derived
through double integrations. The main advantages are
(1).The unsymmetric influence matrix in the conventional BEM can be avoided,
(2).The coupling use with FEM can be easily implemented, and
(3).The storage space in memory can be saved, and the solutions can be obtained more
efficiently and accurately.
The main challenge is that double integrations for the singular and hypersingular kernels
should be dealt with. Two approaches, coordinate transformation and separation
of variables, are
considered. For the former one, the two-point functions for the four kernel
functions can be reduced to difference-type kernels by coordinate transformation.
For the latter one, the kernel functions can be separated into dual series and
the field point and source point in kernel can be uncoupled. Therefore, double integrations can
be easily calculated by two single integrals. In order to check the influence matrices,
not only the test of constant potential but
also equilibrium condition will be employed. A general program was developed
for the Laplace equation.
In addition, the spectral properties for the four kernels are examined and their
orders of pseudo-differential operatorare are determined by an circular example.
Finally, several examples will be demonstrated. The comparisons with the conventional
BEM and the symmetric BEM on memory storage, efficiency, and accuracy will be discussed.
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