无网格伽辽金法在静电场中的应用

Application of EFGM to Numerical Computations of Electrostatic Field

无网格伽辽金法(EFGM)是近几年发展起来的与有限元相似的数值算法,并在电磁场分析中得到初步的应用。本文采用移动的最小二乘法构造形函数,从能量泛函的弱变分形式中得到控制方程,并用Lagrange乘子处理本质边界条件,从而得到数值解。基于MATLAB平台实现了一维静电场中的EFGM算法,并与解析解进行比较,结果表明了EFGM算法的正确性和有效性。

Element free Galerkin method,similar to FEM,is a new numerical method,and is initially applied to the electromagnetic field.In this paper,shape function is constructed by moving least squares method.Control equations are produced from the weak form of variational equation.Lagrange multipliers are used to satisfy essential boundary conditions,the numerical solutions are made out.And a one-dimensional electrostatic example programmed in MATLAB is given to show that the algorithm is correct and effective.