The FMM accelerated PIES with the modified binary tree in solving potential problems for the domains with curvilinear boundaries

Abstract The paper presents an accelerating of solving potential boundary value problems (BVPs) with curvilinear boundaries by modified parametric integral equations system (PIES). fast multipole method (FMM) known from the literature was included into PIES. To consider complex shapes a boundary, modification binary tree used FMM is proposed. combined PIES, called also allows significant reduction random access memory (RAM) utilization. Therefore, it possible to solve engineering on standard personal computer (PC). proposed algorithm based PIES and for obtaining accurate solutions BVPs described at reasonable time PC.