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.

通过改进的参数积分方程系统（PIES），提出了加速解决具有曲线边界的潜在边值问题（BVP）的方法。文献中已知的快速多极方法（FMM）已包括在改进的PIES中。为了考虑边界的复杂曲线形状，提出了对FMM使用的二叉树的修改。FMM与PIES相结合，称为快速PIES，还可以显着降低随机存取存储器（RAM）的利用率。因此，可以解决标准个人计算机（PC）上的复杂工程问题。所提出的算法基于修改后的PIES，并允许在合理的时间在PC上获得由曲线边界描述的复杂BVP的精确解。