A simple technique to improve computational efficiency of meshless methods

Abstract

In order to improve computational efficiency of meshless methods based on Galerkin weak form, in the paper a simple technique is proposed, that is, the nodal influence domain of meshless methods is extended to arbitrary shape. Specifically, circle and rectangle nodal influence domains which are primarily used in meshless methods are generalized to arbitrary convex polygon. When the dimensionless size of the nodal influence domain approaches to 1, the Gauss quadrature point only contributes to these nodes in whose background cell the Gauss quadrature point is located. Thus, the band width of stiff matrix decreases obviously. Meanwhile, the node search process is not needed. The results obtained using the current technique have been compared with those obtained using the finite element method and meshless method with rectangle nodal influence domain, and they present that the provided technique not only has high calculation accuracy, but also enhances computational efficiency of meshless methods greatly. In addition, the technique simplifies imposition of essential boundary conditions as that of the finite element method.