The fast parametric integral equations system in an acceleration of solving polygonal potential boundary value problems. (March 2020) - Kużelewski, Andrzej; Zieniuk, Eugeniusz
Highlights: A new fast parametric integral equations system (PIES) is proposed to accelerate polygonal potential boundary value problems solving. The fast multipole method is utilized to accelerate numerical solving of the fast PIES. Modification of the PIES kernels is proposed to efficient implementation of the fast PIES. The accuracy and efficiency of proposed method is verified. Abstract: The paper presents a new way of accelerating of polygonal potential boundary value problems solving by modified parametric integral equations system (PIES). For this purpose, known from the literature, the fast multipole method (FMM) was included into conventional PIES. Therefore the fast PIES method was obtained. FMM combined with conventional PIES also allows a significant reduction of utilization of random access memory (RAM) of the computer. It gives us a possibility of solving the large-scale engineering problems on a standard personal computer (PC). Finally, the paper presents the development of an algorithm for efficient solving of complex boundary value problems on a standard PC instead of supercomputers, which are usually used to accelerate calculations. The proposed algorithm is based on the modified PIES and allows for obtaining accurate solutions in a reasonable time on the PC, which was the main goal of our research.