RT Journal Article
T1 Optimal shape parameter for the solution of elastostatic problems with the RBF method
A1 Simonenko, Stanislav
A1 Bayona Revilla, Víctor
A1 Kindelan Segura, Manuel
AB Radial basis functions (RBFs) have become a popular method for the solution of partial differential equations. In this paper we analyze the applicability of both the global and the local versions of the method for elastostatic problems. We use multiquadrics as RBFs and describe how to select an optimal value of the shape parameter to minimize approximation errors. The selection of the optimal shape parameter is based on analytical approximations to the local error using either the same shape parameter at all nodes or a node-dependent shape parameter. We show through several examples using both equispaced and nonequispaced nodes that significant gains in accuracy result from a proper selection of the shape parameter.
PB Springer
SN 0022-0833
YR 2014
FD 2014-04-01
LK https://hdl.handle.net/10016/31960
UL https://hdl.handle.net/10016/31960
LA eng
NO This work was supported by Spanish MICINN Grants FIS2011-28838 and CSD2010-00011 and by Madrid Autonomous Region Grant S2009-1597. M.K. acknowledges Fundación Caja Madrid for its financial support.
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RD 26 jun. 2024