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arXiv · 1204.3105

Alternative Tilings for the Fast Multipole Method on the Plane

Yuancheng Luo·Ramani Duraiswami
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Abstract

The fast multipole method (FMM) performs fast approximate kernel summation to a specified tolerance $\epsilon$ by using a hierarchical division of the domain, which groups source and receiver points into regions that satisfy local separation and the well-separated pair decomposition properties. While square tilings and quadtrees are commonly used in 2D, we investigate alternative tilings and associated spatial data structures: regular hexagons (septree) and triangles (triangle-quadtree). We show that both structures satisfy separation properties for the FMM and prove their theoretical error bounds and computational costs. Empirical runtime and error analysis of our implementations are provided.

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Yuancheng Luo, Ramani Duraiswami. 2012-04-13. Alternative Tilings for the Fast Multipole Method on the Plane. https://arxiv.org/abs/1204.3105

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