Fast N-Body Methods: Why, What, and Which.

Why do they matter? Applications abound, even to the extent that fast N-body methods merit a place in the core of numerical analysis. Why are they fast? The basis for all fast N-body solvers is (i) a separable approximation for a pairwise interaction kernel and (ii) exploitation of the associativity (and distributivity) of linear transformations. What are the various N-body methods? Kernel splitting and hierarchical clustering are the two fundamental paradigms. Which is the best N-body method? For molecular biophysics and structural biology, multilevel summation is suggested. [ABSTRACT FROM AUTHOR]