Abstract
An improved weakly-singular form of the hypersingular boundary integral equation (HBIE) for 3-D acoustic wave problems is presented in this paper. Compared with the weakly-singular form of the HBIE published earlier [Y.J. Liu and F.J. Rizzo, A weakly-singular form of the hypersingular boundary integral equation applied to 3-D acoustic wave problems, Comput. Methods Appl. Mech. Engrg. 96 (1992) 271–287], this new form involves only tangential derivatives of the density function and thus its discretization using the boundary element method (BEM) is easier to perform. Instead of using nonconforming and C 1 continuous boundary elements advocated earlier, C 0 continuous (conforming quadratic) elements are employed in the discretization of this weakly-singular form of the HBIE. Some justifications on using C 0 elements for HBIEs are provided to reflect the current views on this crucial issue for HBIEs. It is postulated that the original C 1,α continuity requirement for the density function in the analytical HBIE formulation can be relaxed to piecewise C 1,α continuity in the numerical implementation of the weakly-singular forms of the HBIE. Numerical examples of both scattering and radiation problems clearly demonstrate the accuracy and versatility of the new weakly-singular form of the HBIE for 3-D acoustics.
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