Optimal constant shape parameter for multiquadric based RBF-FD method

JOURNAL OF COMPUTATIONAL PHYSICS

卷:230

Article

Bayona, Victor¹  Moscoso, Miguel¹  Kindelan, Manuel¹ 

[1] Univ Carlos III Madrid, Gregorio Millan Inst, Leganes 28911, Spain

关键词: Radial basis functions;    Multiquadric;    Mesh-free;    Shape parameter;   

DOI  :  10.1016/j.jcp.2011.06.005

来源: Elsevier

【 摘 要 】

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. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free