On the imposition of essential boundary conditions in natural neighbour Galerkin methods

In this paper issues related to the imposition of essential boundary conditions in Natural Neighbour Galerkin methods are addressed. Both Sibson and non-Sibson interpolants ability to exactly reproduce essential boundary conditions is investigated and a new analytical condition ensuring linear precision along explicitly described (i.e. CAD) boundaries in both two and three dimensions is presented. The paper is completed with some benchmark numerical examples. Copyright © 2003 John Wiley & Sons, Ltd.

[1]  David Eppstein,et al.  The Crust and the beta-Skeleton: Combinatorial Curve Reconstruction , 1998, Graph. Model. Image Process..

[2]  B. Moran,et al.  C1natural neighbor interpolant for partial differential equations , 1999 .

[3]  Cecil Armstrong,et al.  Hexahedral meshing using midpoint subdivision and integer programming. , 1995 .

[4]  David G. Kirkpatrick,et al.  On the shape of a set of points in the plane , 1983, IEEE Trans. Inf. Theory.

[5]  V. D. Ivanov,et al.  The non-Sibsonian interpolation : A new method of interpolation of the values of a function on an arbitrary set of points , 1997 .

[6]  V. Mow,et al.  Biphasic creep and stress relaxation of articular cartilage in compression? Theory and experiments. , 1980, Journal of biomechanical engineering.

[7]  Manuel Doblaré,et al.  Imposing essential boundary conditions in the natural element method by means of density-scaled?-shapes , 2000 .

[8]  Wing Kam Liu,et al.  Admissible approximations for essential boundary conditions in the reproducing kernel particle method , 1996 .

[9]  Marshall W. Bern,et al.  A new Voronoi-based surface reconstruction algorithm , 1998, SIGGRAPH.

[10]  R. Sibson.  A vector identity for the Dirichlet tessellation , 1980, Mathematical Proceedings of the Cambridge Philosophical Society.

[11]  Elías Cueto,et al.  Modelling three‐dimensional piece‐wise homogeneous domains using the α‐shape‐based natural element method , 2002 .

[12]  Antonio Huerta,et al.  Enrichment and coupling of the finite element and meshless methods , 2000 .

[13]  Kokichi Sugihara,et al.  Two Generalizations of an Interpolant Based on Voronoi Diagrams , 1999, Int. J. Shape Model..

[14]  T. Belytschko,et al.  THE NATURAL ELEMENT METHOD IN SOLID MECHANICS , 1998 .

[15]  Mark A Fleming,et al.  Meshless methods: An overview and recent developments , 1996 .

[16]  Herbert Edelsbrunner,et al.  Three-dimensional alpha shapes , 1994, ACM Trans. Graph..

[17]  B. Moran,et al.  Natural neighbour Galerkin methods , 2001 .