Efficiency improvement of the polar coordinate transformation for evaluating BEM singular integrals on curved elements

By combining the proposed two transformations with the Guiggiani method in Guiggiani et al. (1992) [8], one obtains an efficient and robust numerical method for computing the weakly, strongly and hyper-singular integrals in high-order BEM. Numerical integration results show that, compared with the original PCT, the present method can reduce the number of quadrature points considerably, for given accuracy. For further verification, the method is incorporated into a 2-order Nystrom BEM code for solving acoustic Burton-Miller boundary integral equation. It is shown that the method can retain the convergence rate of the BEM with much less quadrature points than the existing PCT.