N. Sukumar1, J. E. Bolander1
CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 691-706, 2003, DOI:10.3970/cmes.2003.004.691
Abstract In this paper, we explore the numerical approximation of discrete differential operators on non-uniform grids. The Voronoi cell and the notion of natural neighbors are used to approximate the Laplacian and the gradient operator on irregular grids. The underlying weight measure used in the numerical computations is the {\em Laplace weight function}, which has been previously adopted in meshless Galerkin methods. We develop a difference approximation for the diffusion operator on irregular grids, and present numerical solutions for the Poisson equation. On regular grids, the discrete Laplacian is shown to reduce to the classical finite difference scheme. Two techniques to… More >
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