RT Journal Article
T1 RBF-FD Formulas and Convergence Properties
A1 Bayona Revilla, Víctor
A1 Moscoso, Miguel
A1 Carretero Cerrajero, Manuel
A1 Kindelan Segura, Manuel
AB The local RBF is becoming increasingly popular as an alternative to the global version that suffers from ill-conditioning. In this paper, we study analytically the convergence behavior of the local RBF method as a function of the number of nodes employed in the scheme, the nodal distance, and the shape parameter. We derive exact formulas for the first and second derivatives in one dimension, and for the Laplacian in two dimensions. Using these formulas we compute Taylor expansions for the error. From this analysis, we find that there is an optimal value of the shape parameter for which the error is minimum. This optimal parameter is independent of the nodal distance. Our theoretical results are corroborated by numerical experiments.
PB Elsevier
SN 0021-9991
YR 2010
FD 2010-11-01
LK https://hdl.handle.net/10016/36143
UL https://hdl.handle.net/10016/36143
LA eng
NO This work has been supported by Spanish MECD Grants FIS2007-62673, FIS2008-04921 and by Madrid Autonomous Region Grant S2009-1597.
DS e-Archivo
RD 1 sept. 2024