势问题的复变量无单元Galerkin方法  

Complex variables element-free Galerkin method for potential problems

作　　者：刘沛[1] 彭妙娟[1] 程玉民[2] 

机构地区：[1]上海大学土木工程系,上海200072 [2]上海大学上海市应用数学和力学研究所,上海200072

出　　处：《计算机辅助工程》2009年第4期10-14,共5页Computer Aided Engineering

基　　金：国家自然科学基金(10871124);上海市教育委员会科研创新项目(09ZZ99)

摘　　要：为提高无单元Galerkin(Element-Free Galerkin,EFG)方法的计算效率,将复变量移动最小二乘法与EFG方法结合,利用控制方程的积分弱形式并采用Lagrange乘子法引入边界条件,提出势问题的复变量无单元Galerkin(Complex Variable EFG,CVEFG)方法,并推导相关公式.与传统的EFG方法相比,该方法采用复变量移动最小二乘法可以减少试函数中的待定系数,从而减少计算量、提高计算效率.最后,给出数值算例验证该方法的有效性.To improve the computing efficiency of Element-Free Galerkin （EFG） method, a Complex Variable EFG（CVEFG） method is presented and the corresponding formula are deduced. For the method, complex variable moving least-square approximation is combined with EFG, the integral weak form of control equations is used, and Lagrange multipliers are introduced into the boundary conditions. Compared with the traditional EFG method, the use of complex variables moving least-square approximation can decrease the number of the undetermined coefficients, so it results in the decrease of computation cost and improve the computation coefficient. The numerical examples are given to verify the efficiency of the method.

关 键 词：无网格方法 复变量移动最小二乘法 复变量无单元Galerkin方法 势问题 

分 类 号：O241.5[理学—计算数学] O242[理学—数学]