CAJ | 학술논문

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。
무망격법작위일충신형수치방법，정도고、자괄응분석용역，피면료복잡적망격생성과정，재계산역학영역응용엄범。상시장무망격산법용우점원이유전장적계산，종점원이유변분문제출발대입이동최소이승근사구조적형함수，추도료여지대응적무망격총체구진표체식병용함배경망격적고사적분장기리산화；통과일개간단적이층모형산례험증료산법적정학성。
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.