A collocation mesh-free method based on multiple basis functions

作者：Mohamed H A; Bakrey A E; Ahmed S G^*

来源：Engineering Analysis with Boundary Elements, 2012, 36(3): 446-450.

DOI：10.1016/j.enganabound.2011.09.002

• Moving least squares
• Radial basis function
• Linear interpolation

Two dominant shape functions are used to approximate scattered points in mesh-free methods, e.g. the interpolating radial basis RBF) and the approximating moving least squares (MLS). In the present paper, a new shape function is developed as a linear interpolating function of both MLS and RBF. This function inherits the properties of both MLS and RBF and is regularized by a control parameter mu which takes different values in the domain [0,1]. Based on the proposed shape function, the collocation method is applied to solve initial and boundary value problems in one and two dimensions. The present method gives good results and achieves good convergence trends for different values of mu, compared with MLS and RBF individually, for a large number of nodes.

• 出版日期2012-3