Improved Computational Efficiency of Nearest-Nodes Finite Element Method (NN-FEM)

The recently developed nearest-nodes finite element method (NN-FEM) has a number of advantages over the conventional finite element method (FEM). The most attractive one is that its performance is nearly not affected by element distortion. However, low computational efficiency of NN-FEM is a major concern, as in the original NN-FEM a local problem has to be solved at each quadrature point to construct shape functions there. In this paper, a new strategy is introduced in NN-FEM for constructing shape functions aiming at improving its computational efficiency. The strategy is, for regular-shape elements, shape functions are constructed at the element center and the obtained shape functions are used at all quadrature points in the element; only for severely distorted elements, shape functions are constructed separately at each quadrature point. Numerical results show that computational efficiency of the NN-FEM can be significantly improved with the above strategy, while other performance of the method is not affected.