Uppsala University Department of Information Technology

Technical Report 2014-011

A Task Parallel Implementation of an RBF-generated Finite Difference Method for the Shallow Water Equations on the Sphere

Martin Tillenius, Elisabeth Larsson, Erik Lehto, and Natasha Flyer

April 2014

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.

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