The natural element method (NEM) is a new numerical computational method based on Voronoi diagramand Delaunay triangulation. It is a Galerkin-based meshless method that is builtupon the notion of the natural neighbor interpolation. The naturalelement method has advantages of both finiteelement method and meshless method, and does not have theirdisadvantages. As its shape functionssatisfy interpolating properties, the natural element method is similarto the finite element method and canexactly interpolate piece-wise linear boundary conditions. Themeshless methods, based on moving least square approximation as trialand test functions, can always exactly reproduce essential boundaryconditions. As a meshless method, the natural element method caneasily treat some problems, such as moving boundary and large deformation problems, which finiteelement method is difficult to treat. The essential difference of the natural element method and othernumerical methods is their trial and test functions. Using the natural neighbor interpolation in a Galerkinprocedure, we obtain the natural element Galerkin method based on Voronoi Structure. There are twonatural neighbor interpolants: natural neighbor-based Sibson interpolation and Laplace interpolation(non-Sibsonian interpolation). Laplace interpolation is easier than Sibson interpolation in computation.In its numerical implementation, the natural element method based on Laplace interpolation as trial and testfunctions is easier than that based on Sibson interpolation.In this paper, the basic ideas of natural neighbor-based interpolationand the natural element methodbased on Voronoi structure are presented. The recent advances in the natural neighborinterpolation and the natural element method are reviewed. Someproblems that have to be solved for NEM in the futureare discussed.
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