A task parallel implementation of an RBF-generated finite difference method for the shallow water equations on the sphere✩

Radial basis function-generated finite difference (RBF-FD) methods have recently been proposed as very interesting for global scale geophysical simulations, and have been shown to outperform established pseudo-spectral and discontinuous Galerkin methods for shallow water test problems. In order to be competitive for very large scale simulations, the implementation of the RBF-FD methods needs to be efficient and adapted for modern multicore based computer architectures. The main computational operations in the method consist of unstructured sparse matrix-vector multiplications, which are in general not well suited for multicore-based computers. In this work, the method is implemented for clusters of multicore computers using a task-based parallel programming model. Performance experiments showed that our implementation achieves 71% of theoretical speedup within one computational node, and 90–100% of linear speedup between nodes. A speedup of 178 times compared with the original MATLAB implementation was achieved for a global shallow water problem with a 30km resolution.