Applied Mathematics Colloquium

THE DEPARTMENT OF MATHEMATICAL SCIENCES AND
THE CENTER FOR APPLIED MATHEMATICS AND STATISTICS,
NEW JERSEY INSTITUTE OF TECHNOLOGY

11:30 AM
Friday, May 2, 2003

Cullimore Hall Lecture Room II
New Jersey Institute of Technology





Robert Krasny

Department of Mathematics
University of Michigan

" An Adaptive Treecode for Particle Interactions "

Consider a system of $N$ particles interacting through a long-range potential, e.g. point charges, point masses, or point vortices. The cost of evaluating the pairwise interactions is $O(N^2)$, which is prohibitively expensive when $N$ is large, and a number of hierarchical tree algorithms have been developed to reduce the cost to $O(N\log N)$ or $O(N)$. These include the Barnes-Hut treecode and the Greengard-Rokhlin fast multipole method. The algorithms are recursive and they replace the particle-particle interactions by suitably chosen particle-cluster or cluster-cluster interactions. This talk will review the structure of a treecode algorithm and describe a new variation that emphasizes adaptivity. The new algorithm uses multidimensional Cartesian Taylor expansions in place of spherical harmonics expansions. Applications will be presented to vortex sheet roll-up in fluid dynamics and electrostatic potential/force evaluation in molecular dynamics. This is joint work with Zhong-Hui Duan (University of Akron), Hans Johnston (University of Michigan), and Keith Lindsay (NCAR).