35th Meeting of the AAS Division on Dynamical Astronomy, April 2004
Session 4 Posters I
, Wednesday, April 21, 2004, 7:00-8:30pm,

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[4.07] New Algorithms for Magnetohydrodynamics and Gravity that Emphasize Resolution and Speed.

J. Maron (University of Rochester), T. Dennis (University of Iowa), G. Howes (University of California at Berkeley), A. Brandenburg (Nordic Institute for Theoretical Physics), B. Chandran (University of Iowa), E. Blackman (University of Rochester)

The Gradient Particle Magnetohydrodynamics (GPM) algorithm combines the strengths of an adaptive grid code (AMR) and a smoothed particle code (SPH) by instilling grid-quality gradients into a Lagrangian particle code. It is of particular utility for disk/jet systems.

The hypergradient code uses high-precision tuned finite differences to achieve spectral-quality resolution with 5 times the speed of a spectral code. The finite differencing is not based on a high-order polynomial fit. The polynomial scheme has supurb accuracy for low-wavenumber gradients but fails at high wavenumbers. We instead use a scheme tuned to enhance high-wavenumber accuracy at the expense of low wavenumbers, although the loss of low-wavenumber accuracy is negligibly slight. A tuned gradient is capable of capturing all wavenumbers up to 80 percent of the Nyquist limit with an error of no worse than 1 percent. The fact that gradients are based on finite differences enables diverse geometries to be considered and eliminates the parallel communications bottleneck.

The gravity algorithm is based on the Barnes-Hut tree. It evades the latencies associated with memory accesses, divides, and square roots by grouping bundles of particles together into a simultaneous treewalk and using a polynomial series to approximate the divides and square roots. The algorithm runs 10 times faster than the standard tree codes with no loss of accuracy and it works for individual timesteps.

If you would like more information about this abstract, please follow the link to www.alumni.caltech.edu/~maronj/research.html. This link was provided by the author. When you follow it, you will leave the Web site for this meeting; to return, you should use the Back comand on your browser.

The author(s) of this abstract have provided an email address for comments about the abstract: maron@tapir.caltech.edu

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Bulletin of the American Astronomical Society, 36 #2
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