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On the optimum support size in meshfree methods: a variational adaptivity approach with maximum-entropy approximants
Rosolen, Adrián; Millán, Daniel; Arroyo Balaguer, Marino
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. LACÀN - Centre Específic de Recerca de Mètodes Numèrics en Ciències Aplicades i Enginyeria
We present a method for the automatic adaption of the support size of meshfree basis functions in the context of the numerical approximation of boundary value problems stemming from a minimum principle. The method is based on a variational approach, and the central idea is that the variational principle selects both the discretized physical fields and the discretization parameters, here those defining the support size of each basis function. We consider local maximum-entropy approximation schemes, which exhibit smooth basis functions with respect to both space and the discretization parameters (the node location and the locality parameters). We illustrate by the Poisson, linear and non-linear elasticity problems the effectivity of the method, which produces very accurate solutions with very coarse discretizations and finds unexpected patterns of the support size of the shape functions. Copyright 2009 John Wiley & Sons, Ltd.
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
Meshfree methods (Numerical analysis)
Differential equations, Partial
Mathematical optimization
Anàlisi numèrica
Optimització matemàtica
Equacions diferencials
Attribution-NonCommercial-NoDerivs 3.0 Spain
Wiley and Sons

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