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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| Vydáno v: | Acta numerica Ročník 24; s. 215 - 258 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Cambridge, UK
Cambridge University Press
01.05.2015
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| Témata: | |
| ISSN: | 0962-4929, 1474-0508 |
| On-line přístup: | Získat plný text |
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| 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. |
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| AbstractList | 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. |
| Author | Fornberg, Bengt Flyer, Natasha |
| Author_xml | – sequence: 1 givenname: Bengt surname: Fornberg fullname: Fornberg, Bengt email: fornberg@colorado.edu organization: Department of Applied Mathematics, University of Colorado, Boulder, CO 80309, USA E-mail: fornberg@colorado.edu – sequence: 2 givenname: Natasha surname: Flyer fullname: Flyer, Natasha email: flyer@ucar.edu organization: Institute for Mathematics Applied to Geosciences, National Center for Atmospheric Research, Boulder, CO 80305, USA E-mail: flyer@ucar.edu |
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| Title | Solving PDEs with radial basis functions |
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