A natural neighbour Galerkin method with quadtree structure

Abstract

We describe in this paper a highly structured numerical method that allows for an important speedup in the calculations. The method is implemented in a bi-dimensional binary tree (quadtree or octree) structure in a partition of unity framework. The partition of unity is constructed by using natural neighbour interpolation. Data can be easily obtained from voxel or pixel-based images, as well as STL files or other CAD descriptions. The method described here possesses linear completeness at least and essential boundary conditions are implemented through the characteristic function method, by employing a special class of functions called R-functions. After the theoretical description of the method, some examples of its performance are presented and analysed. Copyright © 2005 John Wiley & Sons, Ltd.