Radial Basis Function - Generated Finite Differences for scientific computing: Freedom from meshes with low computational cost

Natasha Flyer
Institute for Mathematics Applied to Geosciences
University Corporation for Atmospheric Research (UCAR)
Boulder, Colorado, USA


Radial Basis Function-generated Finite Differences (RBF-FD) are gaining popularity in the geosciences due to their competitive accuracy, natural extension into higher dimensions, and low computational complexity and cost. With high-order accuracy (6th to 10th order is common), they also parallelize naturally on multi-core architectures. The method differs from classical finite differences in that the weights for the differentiation matrices are calculated by enforcing that derivative approximations are exact for a linear combination of n-dimensional RBFs rather than one-dimensional polynomials. We will show a variety of test examples in the geosciences that illustrate the versatility, accuracy and computational efficiency of the method. Demonstrations will include benchmarks against other commonly used numerical methods in geoscience modeling as well as performance on Graphics Processing Unit (GPU) accelerator-based computing clusters