This paper presents a so-called hierarchical-element method that can be used to accelerate complex contour dynamics simulations. The method is based on a modified fast multipole method where the multipole approximations are replaced by Poisson integrals. In this paper, attention is being paid to the theoretical derivation of the method. Furthermore, numerical and implementation aspects are considered. Various numerical simulations show that the speed-up of the method is significant, while the accuracy of the results is not being influenced.