On the role of polynomials in RBF-FD approximations: II. Numerical solution of elliptic PDEs

AMS Citation:
Bayona, V., N. Flyer, B. Fornberg, and G. A. Barnett, 2017: On the role of polynomials in RBF-FD approximations: II. Numerical solution of elliptic PDEs. Journal of Computational Physics, 332, 257-273, doi:10.1016/j.jcp.2016.12.008.
Date:2017-03-01
Resource Type:article
Title:On the role of polynomials in RBF-FD approximations: II. Numerical solution of elliptic PDEs
Abstract: RBF-generated finite differences (RBF-FD) have in the last decade emerged as a very powerful and flexible numerical approach for solving a wide range of PDEs. We find in the present study that combining polyharmonic splines (PHS) with multivariate polynomials offers an outstanding combination of simplicity, accuracy, and geometric flexibility when solving elliptic equations in irregular (or regular) regions. In particular, the drawbacks on accuracy and stability due to Runge's phenomenon are overcome once the RBF stencils exceed a certain size due to an underlying minimization property. Test problems include the classical 2-D driven cavity, and also a 3-D global electric circuit problem with the earth's irregular topography as its bottom boundary. The results we find are fully consistent with previous results for data interpolation. (C) 2016 Elsevier Inc. All rights reserved.
Peer Review:Refereed
Copyright Information:Copyright 2017 Elsevier.
OpenSky citable URL: ark:/85065/d7p270xs
Publisher's Version: 10.1016/j.jcp.2016.12.008
Author(s):
  • Victor Bayona
  • Natasha Flyer - NCAR/UCAR
  • Bengt Fornberg
  • Gregory A. Barnett
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