H-p clouds—anh-p meshless method
1996; Wiley; Volume: 12; Issue: 6 Linguagem: Inglês
10.1002/(sici)1098-2426(199611)12
ISSN1098-2426
AutoresC. Armando Duarte, J. Tinsley Oden,
Tópico(s)Fluid Dynamics Simulations and Interactions
ResumoA new methodology to build discrete models of boundary-value problems is presented. The h-p cloud method is applicable to arbitrary domains and employs only a scattered set of nodes to build approximate solutions to BVPs. This new method uses radial basis functions of varying size of supports and with polynomial-reproducing properties of arbitrary order. The approximating properties of the h-p cloud functions are investigated in this article and several theorems concerning these properties are presented. Moving least squares interpolants are used to build a partition of unity on the domain of interest. These functions are then used to construct, at a very low cost, trial and test functions for Galerkin approximations. The method exhibits a very high rate of convergence and has a greater flexibility than traditional h-p finite element methods. Several numerical experiments in 1-D and 2-D are also presented. © 1996 John Wiley & Sons, Inc.
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