Astronomy White Papers
Efficient Shadowing of High Dimensional Chaotic Systems with the Large Astrophysical N-body Problem as an Example
Overview N-body systems are chaotic. This means that numerical errors in their solution are magnified exponentially with time, perhaps making the solutions useless. Shadowing tries to show that numerical solutions of chaotic systems still have some validity. A previously published shadowing refinement algorithm is optimized to give speedups of order 60 for small problems and asymptotic speedups of O(N) on large problems. This optimized algorithm is used to shadow N-body systems with up to 25 moving particles. Preliminary results suggest that average shadow length scales roughly as 1/N, ie., shadow lengths decrease rapidly as the number of phase-space dimensions of the system is increased. Some measures of simulation error for N-body systems are discussed that are less stringent than shadowing. Many areas of further research are discussed both for high-dimensional shadowing, and for N-body measures of error.
| Publisher | University of Toronto | File Format | PDF, requires Acrobat Rdr 5 |
|---|---|---|---|
| Date Published | August 2003 | Downloads | 97 |
| Format | White Papers | ||
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