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Solving PDEs with radial basis functions
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DOI：10.1017/S0962492914000130.png)
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摘要
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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.
Keyword:
FINITE-DIFFERENCE SCHEMES
DATA APPROXIMATION SCHEME
SHALLOW-WATER EQUATIONS
SCATTERED DATA
THERMAL-CONVECTION
STABLE COMPUTATION
SPHERICAL-SHELL
MESHLESS METHOD
RBF-FD
INTERPOLATION
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11.3
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89
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