On the optimum support size in meshfree methods: a variational adaptivity approach with maximum entropy approximants

Author (s): Rosolen, A,; Millán, D. and Arroyo, M.
Journal: International Journal for Numerical Methods in Engineering

Volume: 82, Issue 7
Pages: 868 – 895
Date: 2010

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 Poisson, linear and nonlinear 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.



@article {NME:NME2793,
author = {Rosolen, A.; Millán, D. and Arroyo, M.},
title = {On the optimum support size in meshfree methods: A variational adaptivity approach with maximum-entropy approximants},
journal = {International Journal for Numerical Methods in Engineering},
pages = {868--895},
volume = {82},
number = {7},
publisher = {John Wiley & Sons, Ltd.},
issn = {1097-0207},
url = {http://dx.doi.org/10.1002/nme.2793},
doi = {10.1002/nme.2793},
keywords = {meshfree methods, local maximum-entropy approximants, variational adaptivity, support size},
year = {2010},