Abstract
The higher order moment method has far fewer unknowns compared to the low order methods. However, the computation of the self-term matrix elements is extremely time-consuming. This paper presents an algorithm to extract the singularity by dividing the integrand into two parts on account of Taylor's formula. The integrand of the first part with a removable discontinuity is easy to be integrated. The rest part consists of three principal singular functions. Their singularities are canceled by the Jacobian of a simple transformation. This singularity extraction leads to a rapid non-redundant integration. Numerical results prove that this algorithm is more than 20 times faster than the old method.