势问题的复变量无单元Galerkin方法

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.

Complex variable element-free Galerkin method for potential problems

To increase the computing efficiency of element-free Galerkin (EFG) method , combining complex variable moving least-square approximation (CVMLS) with the EFG method, and using the integral weak form of control equations of potential problems, the complex variable element-free Galerkin (CVEFG) method for 2-D potential problems is presented in this paper. And in the CVEFG method, the Lagrange multipliers are applied to enforce the boundary conditions. The corresponding formulae of the CVEFG for two-dimensional potential problems are obtained. Compared with the EFG method, the CVEFG presented in this paper has fewer coefficients, then it results greater precision and lower computation cost. Some examples are given to demonstrate the efficiency of the present method.