A new discrete method for multipolar boundary elements for three-dimensional potential problems

Fast multipolar expansion;  Laplace transform;  potential problems;  Basic solution

The fast multipole expansion method is applied to discretize the boundary equation of the three-dimensional potential problem. Since the basic solution of the boundary equation contains the singular term 1/r, which affects the application of multipolar expansion (FMM), the Laplace transform can be converted into an exponential form sequence. This method avoids the singularity of multipolar expansion, obtains a new discrete analytic formula, and provides a new method for theoretical analysis of multipolar boundary elements.