Singularity treatment of higher-order moment method on NURBS mesh

A new singularity treatment technique of higher-order moment method is proposed to avoid the intensive computation of the Duffy transformation with Gaussian quadrature. We first transform the u-v coordinates of NURBS patch into the polar coordinates and approximate the NURBS expression in the polar coordinates through the expansion of the Bernstein polynomials with Taylor series. Then the singularity is analytically removed and the integral on the NURBS patch can be calculated normally. Numerical results show good efficiency and accuracy of the proposed singularity treatment technique.