Solving PDEs with radial basis functions

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 spect...

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Vydané v:	Acta numerica Ročník 24; s. 215 - 258
Hlavní autori:	Fornberg, Bengt, Flyer, Natasha
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Cambridge, UK Cambridge University Press 01.05.2015
Predmet:	Mathematical functions Numerical analysis
ISSN:	0962-4929, 1474-0508
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Shrnutí:	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.
Bibliografia:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14
ISSN:	0962-4929 1474-0508
DOI:	10.1017/S0962492914000130