RT Journal Article
T1 Optimal constant shape parameter for multiquadric based RBF-FD method
A1 Bayona Revilla, Víctor
A1 Moscoso, Miguel
A1 Kindelan Segura, Manuel
AB Radial basis functions (RBFs) have become a popular method for interpolation and solution of partial differential equations (PDEs). Many types of RBFs used in these problems contain a shape parameter, and there is much experimental evidence showing that accuracy strongly depends on the value of this shape parameter. In this paper, we focus on PDE problems solved with a multiquadric based RBF finite difference (RBF-FD) method. We propose an efficient algorithm to compute the optimal value of the shape parameter that minimizes the approximation error. The algorithm is based on analytical approximations to the local RBF-FD error derived in [1]. We show through several examples in 1D and 2D, both with structured and unstructured nodes, that very accurate solutions (compared to finite differences) can be achieved using the optimal value of the constant shape parameter.
PB Elsevier
SN 0021-9991
YR 2011
FD 2011-08-10
LK https://hdl.handle.net/10016/36145
UL https://hdl.handle.net/10016/36145
LA eng
NO This work has been supported by Spanish MICINN grants FIS2010-18473, CSD2010-00011 and by Madrid Autonomous Region grant S2009-1597.
DS e-Archivo
RD 1 sept. 2024