Thanks a lot for this explanation in details! ______________________________
Anton Gladkyy 2010/4/27 Václav Šmilauer <[email protected]> > > 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 > > > _______________________________________________ > Mailing list: > https://launchpad.net/~yade-dev<https://launchpad.net/%7Eyade-dev> > Post to : [email protected] > Unsubscribe : > https://launchpad.net/~yade-dev<https://launchpad.net/%7Eyade-dev> > More help : https://help.launchpad.net/ListHelp >
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