A study on the performance of natural neighbour-based Galerkin methods

In this paper we address the problem of improving natural element simulations in terms of computational cost. Several problems are discussed, that include an efficient natural neighbour search algorithm and a comparison of different natural neighbour-based interpolation algorithms. In particular, we review the so-called pseudo-NEM, a moving least squares-like approximation scheme that employs natural neighbours, and compare it with traditional Sibson and Laplace interpolation schemes in terms of both accuracy and computational cost. Some examples in linear Elasticity and visco-plasticity are analysed in order to test the proposed schemes in engineering problems. Copyright q 2007 John Wiley & Sons, Ltd.