点源二维电场变分问题的无网格解法

摘要

无网格法作为一种新型数值方法，精度高、自适应分析容易，避免了复杂的网格生成过程，在计算力学领域应用广泛。尝试将无网格算法用于点源二维电场的计算，从点源二维变分问题出发代入移动最小二乘近似构造的形函数，推导了与之对应的无网格总体矩阵表达式并用含背景网格的高斯积分将其离散化；通过一个简单的二层模型算例验证了算法的正确性。%The mesh⁃free method, as a new numerical method which avoids the mesh generation and possesses the advantages of high precision and simple adaptive analysis, has been widely used in the field of computational mechanics. In this paper, the authors attempt to calculate the point source two⁃dimensional electric field by using mesh⁃free method. The moving least square approximation theory is introduced and stiffness matrix of mesh⁃free method is deduced into shape function structured by moving least squares approximation corresponding to the point source two⁃dimensional variational problem, and the expression is discretized by Gauss integral containing background grid. At last, the validity of the algorithm is verified by a simple calculation of two⁃dimensional model.