Fast Algorithm to Extract the Singularity of Higher Order Moment Method

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.