Abstract
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.
Highlights
It is a known fact that to obtain accurate results of modelling and solving boundary value problems (BVPs), the appropriate method should be applied
The paper presents a new way of accelerating computations and reducing random access memory (RAM) utilization of the parametric integral equations system (PIES) applied to solve complex curvilinear potential 2D BVPs
To verify the proposed concept, the fast multipole method (FMM) is included into the PIES with modified kernels and the fast PIES is obtained
Summary
It is a known fact that to obtain accurate results of modelling and solving boundary value problems (BVPs), the appropriate method should be applied. To improve the accuracy of solutions, remodelling of the shape of the boundary is unnecessary [15] contrary to the BEM and the FEM where the process of discretization should be repeated The former studies confirmed the accuracy of the PIES in solving 2D and 3D engineering problems in comparison to the analytical and classical numerical methods, e.g. The main goal of this paper is to present the FMM accelerated PIES (called the fast PIES) applied for numerical solving of complex curvilinear 2D potential BVPs. The FMM algorithm and the binary tree are modified to allow solving the problems with the complex shape of a boundary. The efficiency and accuracy of the fast PIES are tested on curvilinear 2D potential BVPs
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