RT Journal Article
T1 On the role of polynomials in RBF-FD approximations: II. numerical solution of elliptic PDEs
A1 Bayona Revilla, Víctor
A1 Flyer, Natasha
A1 Fornberg, Bengt
A1 Barnett, Gregory A.
AB 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.
PB Elsevier
SN 0021-9991
YR 2017
FD 2017-03-01
LK https://hdl.handle.net/10016/31935
UL https://hdl.handle.net/10016/31935
LA eng
NO The National Center for Atmospheric Research is sponsored by the NSF. Victor Bayona was a post-doctoral fellow funded by the Advanced Study Program at the National Center for Atmospheric Research during the majority of this work.
DS e-Archivo
RD 1 sept. 2024