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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| Published in: | Acta numerica Vol. 24; pp. 215 - 258 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Cambridge, UK
Cambridge University Press
01.05.2015
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| Subjects: | |
| ISSN: | 0962-4929, 1474-0508 |
| Online Access: | Get full text |
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| Summary: | 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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| Bibliography: | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 |
| ISSN: | 0962-4929 1474-0508 |
| DOI: | 10.1017/S0962492914000130 |