Solving PDEs with radial basis functions

AMS Citation:
Fornberg, B., and N. Flyer, 2015: Solving PDEs with radial basis functions. Acta Numerica, 24, 215-258, doi:10.1017/S0962492914000130.
Date:2015-05-01
Resource Type:article
Title:Solving PDEs with radial basis functions
Abstract: Finite differences provided the first numerical approach that permitted large-scale simulations in many applications areas, such as geophysical fluid dynamics. As accuracy and integration time requirements gradually increased, the focus shifted from finite differences to a variety of different spectral methods. During the last few years, radial basis functions, in particular in their 'local' RBF-FD form, have taken the major step from being mostly a curiosity approach for small-scale PDE 'toy problems' to becoming a major contender also for very large simulations on advanced distributed memory computer systems. Being entirely mesh-free, RBF-FD discretizations are also particularly easy to implement, even when local refinements are needed. This article gives some background to this development, and highlights some recent results.
Peer Review:Refereed
Copyright Information:Copyright 2015 Cambridge University Press.
OpenSky citable URL: ark:/85065/d75h7htg
Publisher's Version: 10.1017/S0962492914000130
Author(s):
  • Bengt Fornberg
  • Natasha Flyer - NCAR/UCAR
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