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• W83790780 abstract "Abstract: This work introduces a procedure for auto-mated determination of weight function free parametersin moving least squares (MLS) based meshless meth-ods for non-uniform grids. The meshless method usedin present work is Diffuse Approximate Method (DAM).The DAM is structured in 2D with the one or two pa-rameter Gaussian weigh function, 6 polynomial basisand 9 noded domain of influence. The procedure con-sists of three main elements. The first is definition ofthe reference quality function which measures the differ-ence between the MLS approximation on non-uniformand hypothetic uniform node arrangements. The secondis the construction of the object function from the refer-ence quality function which has to be minimized for op-timum performance of the method on non-uniform nodearrangement. The third is the optimization procedure forobtaining the minimum of the object function. The mainidea of this paper is demonstrated on solution of the tran-sient Burgers equation on stretched non-uniform grid andthree types of random non-uniform grids. The inverseGauss function is used as a reference quality function,object function is built from the second partial deriva-tives, and the k-ary heap like tree procedure is used foroptimization. A substantial improvement of the accuracyof the method is achieved with the locally optimized val-ues of the weight function compared to the fixed valuethat was exclusively used in previous DAM literature.With statistical comparison it was shown that in additionto improvement of accuracy also the stability of simula-tion is substantially improved.keyword: Optimization, shape parameters, meshlessmethods, Diffuse Approximate Method." @default.
• W83790780 created "2016-06-24" @default.
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• W83790780 date "2007-05-01" @default.
• W83790780 modified "2023-09-23" @default.
• W83790780 title "Weight Function Shape Parameter Optimization in Meshless Methods for Non-uniform Grids" @default.
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• W83790780 doi "https://doi.org/10.3970/cmes.2007.019.055" @default.
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