基于局部基本解法的静电场仿真分析

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

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。

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.