yade-dev team mailing list archive

[Anton Gladky <gladky.anton@xxxxxxxxx>]

Thanks a lot for this explanation in details!
______________________________

Anton Gladkyy


2010/4/27 Václav Šmilauer <eudoxos@xxxxxxxx>

> > Here https://bugs.launchpad.net/yade/+bug/394687/comments/26
> > You said:
> > "...Just that everybody knows now that slightly different results are
> > OK with openMP (different addition order, hence different rounding; if
> > damping!=0, that can make very different results) and it is not a
> > bug."
> >
> > Could you not explain in a couple of words, why?
> >
> > Can we do something with that?
>
> I thought we've discussed that several times.
>
> In finite precision computations, the order of summation can make the
> result different at least sinificant places; try this in python (will be
> the same in c++):
>
> (1/10.)+(1/13.)+(1/17.)
> (1/17.)+(1/13.)+(1/10.)
>
> you will get
>
> 0.23574660633484162
> 0.23574660633484165
>
> In parallel computation, forces generated by interaction are assigned to
> bodies in quasi-random order. Therefore summary force F on body can be
> different between single-threaded and multi-threaded, and it can also be
> different for different runs of multi-threaded computation depending on
> exact thread scheduling by the kernel (inpredictable).
>
> Cundall's damping changes acceleration on body a=F/m to
>
> ai'=ai(1-d*sgn(Fi*(vi+.5*Δt*ai)), i∈{x,y,z}
>
> where F is force on body, vi is velocity at (t+Δt/2), a is acceleration
> at (t), d is dimensionless damping coefficient (say 0.4). The sgn()
> function is dicontinuous around zero, therefore there is some (small) ε
> that in case |(vi+.5*Δt*ai)|<ε, will make the value of sgn()
> arbitrarily ±1, leading non-deterministically to one of
>
>  ai'=1.4*ai
>  ai'=0.6*ai
>
> Therefore the rounding "error" at least significant places can lead to
> immediate macroscopic effect.
>
> Note: this is different from integration schemes where little change in
> initial conditions makes big difference due to high sensitivity of
> continuous equations (e.g. fractals); the equation involved here is
> really discontinuous.
>
> I will put it to docs somewhere.
>
> v
>
>
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