An application of fast multipole method to isogeometric boundary element method for Laplace equation in two dimensions

According to the concept of isogeometric analysis, we have developed a boundary element method (BEM) using B-spline basis functions for the two-dimensional Laplace equation, focusing on external Neumann problems. Further, we have applied the fast multipole method (FMM) to the present isogeometric BEM to reduce the computational complexity from O(n2)O(n2) to O(n), where n is the number of control points to define the closed boundary of the computational domain. In a benchmark test, we confirmed that the FMM can accelerate the isogeometric BEM successfully. In addition, the proposed fast BEM can be an alternative of the standard fast BEM using the piecewise-constant elements. Finally, the feasibility of the proposed method for solving large-scale problems was demonstrated through numerical examples.