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Choreography in Gravity Simon Portegies Zwart, Jeroen Bedorf, - - PowerPoint PPT Presentation
Choreography in Gravity Simon Portegies Zwart, Jeroen Bedorf, - - PowerPoint PPT Presentation
Choreography in Gravity Simon Portegies Zwart, Jeroen Bedorf, Evghenii Gaburov, Tjarda Boekholt, Michiko Fujii, Tomoaki Ishiyama, Keigo Nitadori An ape on the shoulders of a giant, still is an ape. Larger comuters require more complex
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- More scales leads to more complexity
- More physics leads to more complexity
- More complexity leads to less
understanding Larger comuters require more complex software. But does this lead to a better understanding?
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Therefore Bonsai Small & resilient
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4GPUs = 0.005PFlops 40 GPUs=0.05PFlops 400GPUs=0.5PFflops ~20000GPUs= 25PFflops 4000GPUs=5PFflops Leiden LGM Tsukuba CSCS Piz Daint ORNL Titan
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HPC on Titan's GPU-farm
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10
11 Stars 2×
10
10 years
2.5×10
8 years×100steps×60 operations
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Jeroen Bédorf etal: simulation of Andromeda/Milky Way encounter on Titan
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Hoag's object (HST) Bonsai simulation
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- “Errors in calculations of n-body systems grow
exponentially … and may therefore invalidate the results ...” (Miller 1964)
Being able to perform large calculations is not the same as being able to perform accurate calculations
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BRUTUS
a brute force arbitrary-precision N-body code
- Two ingredients:
- Gragg-Bulirsch-Stoer method
– Modified midpoint method – Richardson extrapolation – Tolerance parameter
- Arbitrary-Precision arithmetic
– Number of significant digits Tjarda Boekholt
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Red: dE/E <10-74 Black: dE/E <10-11
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Exponential divergence
δ = 0.5 log10 1/(6N) ∑ (x2-x1)2 + (v2-v1)2
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10,000 realizations of N=3 give no systematic bias
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Conclusions
- While computers get bigger
software gets more complex
- Continuing trend in more
demanding simulations
- By keeping codes small and