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Radial Basis Function-Generated Finite Differences (RBF-FD): New Computational Opportunities in the Geosciences

A novel mathematical methodology is presented for modeling a wide array of physics in the geosciences. It based on a mesh-less approach known as radial basis function -generated finite differences. Due to its independence of any grids or mappings for irregular geometries (as is needed with finite difference, volume or element methods), where the physics is resolved can be directly connected to where the observational data is sampled. As a result, it gives far better physical representations than any other methods at coarser resolutions, allowing the data to be better assimilated for initialization of models. Furthermore, it uses the same basis functions as that those used in spatial geostatistics, allowing for a more unified mathematical framework in quantifying uncertainties. Due to the structure of the resulting matrices, it scales extremely well on accelerator computer architectures. It is currently being considered at NOAA, and the European Centre for Medium-Range Weather Forecasting (ECMWF), and NCAR. Examples will be given from a variety of geoscience fields.
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