Data Structures, Optimal Choice of Parameters, and Complexity Results for Generalized Multilevel Fast Multipole Methods in d Dimensions

Generalized Multilevel Fast Multipole Methods in d Dimensions Nail A. Gumerov,∗ Ramani Duraiswami,† and Eugene A. Borovikov‡ Perceptual Interfaces and Reality Laboratory, Institute for Advanced Computer Studies, University of Maryland, College Park, Maryland, 20742. Abstract We present an overview of the Fast Multipole Method, explain the use of optimal data structures and present complexity results for the algorithm. We explain how octree structures and bit interleaving can be simply used to create efficient versions of the multipole algorithm in d dimensions. We then present simulations that demonstrate various aspects of the algorithm, including optimal selection of the clustering parameter, the inßuence of the error bound on the complexity, and others. The use of these optimal parameters results in a many-fold speed-up of the FMM, and prove very useful in practice. This report also serves to introduce the background necessary to learn and use the generalized FMM code we have developed.