2000
DOI: 10.1007/s004660050470
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Dispersive properties of the natural element method

Abstract: The Natural Element Method (NEM) is a meshfree numerical method for the solution of partial differential equations. In the natural element method, natural neighbor coordinates, which are based on the Voronoi tesselation of a set of nodes, are used to construct the interpolant. The performance of NEM in two-dimensional linear elastodynamics is investigated. A standard Galerkin formulation is used to obtain the weak form and a centraldifference time integration scheme is chosen for time history analyses. Two dif… Show more

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Cited by 34 publications
(23 citation statements)
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“…In their work, it is presented as a meshless method for the solution of partial di erential equations in the context of elastostatics. Recently, the extension to elastodynamics has also been presented [17].…”
Section: The Natural Element Methodsmentioning
confidence: 98%
See 1 more Smart Citation
“…In their work, it is presented as a meshless method for the solution of partial di erential equations in the context of elastostatics. Recently, the extension to elastodynamics has also been presented [17].…”
Section: The Natural Element Methodsmentioning
confidence: 98%
“…This relies on the concepts of Delaunay triangulations and Dirichlet tesselations [12; 13] to build the shape functions, which are deÿned, in the most general case, over the convex hull of the set of points that form the input of the problem. A deep study of this method in the context of two-dimensional solid mechanics has been made by Sukumar et al [14][15][16][17]. Although showing promising characteristics, like the strictly interpolant behaviour, linear consistency and smoothness of the shape function, the method also presents some drawbacks.…”
Section: Introductionmentioning
confidence: 96%
“…Cho and Lee [12] introduced a Petrov-Galerkin natural element method providing the best convergence rate in unconstrained two-dimensional linear elasticity problems in both convex and non-convex domains. Through the application to linear vibration and wave propagation problems, Bueche et al [14] confirmed that the overall performance of the natural element method in linear elastodynamics is better than the linear finite element method. Martinez et al [15] reported the attractive capabilities of the natural element method to simulate the flow problems involving moving or free boundaries.…”
Section: Introductionmentioning
confidence: 93%
“…Sukumar et al [4,5] applied the NEM to solve various problems in twodimension linear elastostatics to examine its accuracy and robustness, and tried to incorporate the conventional FEM into it. Through the application of the NEM in linear vibration and wave propagation problems, Bueche et al [6] reached a conclusion that its overall performance in linear elastodynamics is better than the linear FEM. Martinez et al [7] used it to simulate the flow problems involving moving of free boundaries.…”
Section: Introductionmentioning
confidence: 98%