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

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