New concepts for moving least squares: An interpolating non-singular weighting function and weighted nodal least squares

In this paper two new concepts for the classical moving least squares (MLS) approach are presented. The first one is an interpolating weighting function, which leads to MLS shape functions fulfilling the interpolation condition exactly. This enables a direct application of essential boundary conditions in the element-free Galerkin method without additional numerical effort. In contrast to existing approaches using singular weighting functions, this new weighting type leads to regular values of the weights and coefficients matrices in the whole domain even at the support points. The second enhancement is an approach, where the computation of the polynomial coefficient matrices is performed only at the nodes. At the interpolation point then a simple operation leads to the final shape function values. The basis polynomial of each node can be chosen independently which enables the simple realization of a p-adaptive scheme.