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Research Activities > Programs > Fast Approximate Algorithms > Derek Richardson

Fast Multipole Method, Tree-Code and Related Approximate Algorithms.
Trading Exactness for Efficiency.

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pkdgrav: A Parallel k-D Tree Gravity Solver for N-Body Problems

Dr. Derek Richardson

Astronomy at University of Maryland

Abstract:   I will present an overview of pkdgrav, a code written at the "N-Body Shop" of the University of Washington by J. Stadel, T. Quinn, and various other authors, including myself. pkdgrav was initially designed for large-scale structure cosmological simulations but has subsequently been modified for a variety of purposes. My specific applications of pkdgrav are tailored around planetesimal dynamics: the gravitational and collisional evolution of small bodies in solar systems. I will discuss the k-D tree structure and its benefits over the generic Barnes & Hut (1986) algorithm for N-body simulations with large dynamic range. Accuracy and efficiency tests will be presented. We have found that, for our specific applications, an expansion to hexadecapole order offers the best tradeoff between force accuracy and execution time. Example simulations in planetesimal dynamics will be presented, and programming challenges encountered for certain models, such as sliding patches and rigid aggregates, will be discussed.