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

CSIC Building (#406), Seminar Room 4122.
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A Treecode Algorithm for Regularized Particle Interactions

Dr. Robert Krasny

Mathematics at University of Michigan

Abstract:   A new version of the Barnes-Hut treecode algorithm will be described for particle simulations of vortex sheet roll-up in 3D fluid flow. The vortex sheet problem requires using a regularized Biot-Savart kernel in order to control the shortwave Kelvin-Helmholtz instability. The treecode algorithm uses Taylor expansions in Cartesian coordinates to approximate the particle-cluster interactions. The necessary Taylor coefficients are computed using a recurrence relation. Adaptive techniques are employed to gain efficiency, including adaptive clusters and variable order expansions. Results will be presented showing the azimuthal instability of a vortex ring. The algorithm is also being applied to electrostatic force evaluation in molecular dynamics and plasma dynamics, and these applications will be briefly described.

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