基于局部基本解法的静电场仿真分析

将局部基本解方法应用于静电场问题的模拟与分析。局部基本解方法是利用控制方程的基本解，基于局部理论和移动最小二乘原理提出的一种无网格算法。相比于有限元和有限差分等传统网格类方法，该方法仅需离散节点，避免了复杂的网格剖分难题。作为一种半解析数值技术，物理问题的基本解被作为插值基函数建立数值离散模型，从而保证了算法的较高精度。此外，与具有全局离散格式的无网格方法相比，局部基本解法更适用于高维复杂几何和大尺度模拟。二维和三维数值试验表明，该方法具有实施方便灵活，计算精度高和计算速度快等优势。为静电场仿真研究开辟新的途径，拓展了局部基本解方法的应用领域。

Simulation Analysis of Electrostatic Field Based on Localized Method of Fundamental Solutions

Localized method of fundamental solutions is applied to the simulation and analysis of electrostatic field problems. The localized method of fundamental solutions is a meshless algorithm based on local theory and moving least square approximation, which uses fundamental solution of the governing equation. Compared with traditional mesh-type methods such as finite element method and finite difference method, this method needs discrete nodes only, and avoids troublesome mesh generation. As a semi-analytical numerical technique, fundamental solutions of physical problems are used as interpolation basis functions to establish a numerical discrete model, thus ensuring high accuracy of the algorithm. In addition, compared with meshless methods with global discretization scheme, the local fundamental method is more suitable for high-dimensional complex geometry and large-scale simulation. Two- and three-dimensional numerical tests show that this method is convenient, flexible, accurate and fast. It is a new way for electrostatic field simulation. It expands application of localized method of fundamental solutions.