基于积分弱形式的无网格-有限元法耦合方法研究

无网格伽辽金法是基于移动最小二乘法的一种求解偏微分方程非常有效的方法,但是对于一些规模较大的问题,其计算费用较高,将无网格法与有限元耦合可以极大提高求解效率.文中根据D. Hegen提出的基于积分弱形式耦合方法,进一步明确处理耦合区域部分的数学、物理意义, 有效地引入一个综合控制因子反映权函数的紧支性, 并经算例验证方法的正确性及控制因子的有效性.

STUDY ON THE EFGM-FEM COUPLING METHOD BASED ON THE WEAK FORMS

Element free Galerkin method(EFGM)is a effective method for solving partial differential equations with the help of shape functions coming from moving least squares approximation.But EFGM is computationally expensive for large-scale problems.It can improve computational efficiency absolutely to couple EFGM with FEM(finite element method).On the basis of several weak forms of the equations brought out by D.Hegen,the mathematical and physical meanings of the coupled part are discussed.A coefficient used to control the relative weight and compact domain is proposed.A numerical example shows the method with the controlling coefficient can compute displacement field accurately and effectively.