Abstract
A weakly singular boundar integral equation and a non-singular one are derived for acoustic problems. By using the one-dimensional wave propagation mode, the degree of the singularities appearing in the conventional boundary integral equation can be reduced. Since the strong singularity is removed in the weakly singular equation, the jump term of the field pressure expression in the very vicinity of the boundary disappears. It is shown that the weak singularity can be also removed for a smooth boundary in the non-singular representation, and thus special treatments for singular integral are no longer needed. In order to test the proposed method, several simple problems have been solved by employing the triangular element with standard Gaussian quadrature integration points. The results obtained show the accuracy of the method in the near field as well as on the boundary.
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