An efficient linear-precision partition of unity basis for unstructured meshless methods

We describe an approach to construct approximation basis functions for mesh less methods, which is based on the concept of a partition of unity. The ap proach has the following properties: (i) the grid consists of scattered nod es, (ii) the basis reproduces exactly complete linear polynomials, (iii) on ly the values of the approximated function at the nodes are used as unknown s, (iv) the construction of the basis is only slightly more expensive than the Shepard constant-precision method, and finally, (v) the method is appli cable in any number of spatial dimensions. Copyright (C) 2000 John Wiley & Sons, Ltd.