A new form of the hypersingular boundary integral equation for 3-D acoustics and its implementation with C0 boundary elements Original Research Article

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 C1 continuous boundary elements advocated earlier, C0 continuous (conforming quadratic) elements are employed in the discretization of this weakly-singular form of the HBIE. Some justifications on using C0 elements for HBIEs are provided to reflect the current views on this crucial issue for HBIEs. It is postulated that the original C1,α continuity requirement for the density function in the analytical HBIE formulation can be relaxed to piecewise C1,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.