[petsc-dev] strangness in Chebyshev estimate of eigenvalues

Tue May 17 13:01:39 CDT 2016

   Since Matt wrote a portable random number generator as the default random number generator there should be no difference on any machine based on using using a random right hand side. 

  Of course, as always, with different number of processes one will get different results, even with Jacobi + Chebyshev because the random numbers generated will be different with different number of processes, is this important?

    I think we should wait to hear from Jed before making any change but I am comfortable with changing the default to use the random number generator.

   Barry

> On May 17, 2016, at 11:21 AM, Mark Adams <mfadams at lbl.gov> wrote:
> 
> 
> On Sat, Aug 22, 2015 at 10:39 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
> 
> > On Aug 22, 2015, at 9:26 PM, Mark Adams <mfadams at lbl.gov> wrote:
> >
> >  I would vote for (1).
> >
> > Also, I hope cheb->random is the default.
> 
>    Well then different machines will produce different convergence histories which is annoying for any kind of "no change" daily testing. Except for you, most of the rest of us don't like the random default, sorry :-)
> 
> Well, this bit me and Garth Wells, among others I would guess.
> 
> The problem is that RHS are often smooth and this leads to poor convergence to the highest eigenvalue. As an example on the new ex56, elasticity, cube, traction on one side, the history of the eigen estimator looks like this (appended). Garth mentioned that he uses 50 iterations in the eigen estimator (ie, a lot), and you can see why here, It looks converged at 44 iterations at ~1.42 and then pops up to ~1.72 very quickly.  This is such a big jump that it overwhelms the common 1.05 safety factor.  If you add -mg_levels_ksp_chebyshev_esteig_random you see nice smooth and fast convergence (appended).
> 
> Note, the iteration number of this jump seems to be about linear in h, so this will fail with 50 iterations on a larger problem (this one has about 6M dof).
> 
> Now, I guess I can put -mg_levels_ksp_chebyshev_esteig_random in the tutorials as suggested parameters and keep them out of the tests to avoid your issue with regression tests.  Right?
> 
> Mark
> ps, I'm sure Jed free climbed out of the pit, so you can use his rope.
> 
> 
>        39 KSP Residual norm 5.149666187461e+00 % max 1.423034674475e+00 min 5.820371669083e-04 max/min 2.444920626003e+03
>        40 KSP Residual norm 5.157885158697e+00 % max 1.423126042184e+00 min 5.557328840496e-04 max/min 2.560809487850e+03
>        41 KSP Residual norm 5.303627521687e+00 % max 1.423199352292e+00 min 5.313351872668e-04 max/min 2.678533977041e+03
>        42 KSP Residual norm 5.364384189061e+00 % max 1.423275534927e+00 min 5.062394822273e-04 max/min 2.811466874659e+03
>        43 KSP Residual norm 5.490412749639e+00 % max 1.423347554528e+00 min 4.823994222923e-04 max/min 2.950558165607e+03
>        44 KSP Residual norm 5.298532106786e+00 % max 1.423435653436e+00 min 4.630735554742e-04 max/min 3.073886721901e+03
>        45 KSP Residual norm 5.250150466693e+00 % max 1.444039693619e+00 min 4.458237353578e-04 max/min 3.239037267632e+03
>        46 KSP Residual norm 5.355091565702e+00 % max 1.597859894587e+00 min 4.296586330882e-04 max/min 3.718905595128e+03
>        47 KSP Residual norm 5.359212994059e+00 % max 1.694500733083e+00 min 4.115503583969e-04 max/min 4.117359391167e+03
>        48 KSP Residual norm 5.382627967217e+00 % max 1.715436978188e+00 min 3.945385500813e-04 max/min 4.347957830318e+03
>        49 KSP Residual norm 5.333511242816e+00 % max 1.719426018108e+00 min 3.791973408295e-04 max/min 4.534383111304e+03
>        50 KSP Residual norm 5.286785239032e+00 % max 1.720488275875e+00 min 3.655323031666e-04 max/min 4.706802274303e+03
> 
> with -mg_levels_ksp_chebyshev_esteig_random
> 
>         0 KSP Residual norm 4.587476885185e+05 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00
>         1 KSP Residual norm 5.000026676130e+05 % max 2.096521908651e-01 min 2.096521908651e-01 max/min 1.000000000000e+00
>         2 KSP Residual norm 2.383418066969e+06 % max 9.808897648348e-01 min 5.952257317564e-03 max/min 1.647929033478e+02
>         3 KSP Residual norm 2.574503036099e+06 % max 1.019204519789e+00 min 3.039124767415e-03 max/min 3.353611969855e+02
>         4 KSP Residual norm 2.458678036734e+06 % max 1.244548092713e+00 min 1.992498130768e-03 max/min 6.246169436720e+02
>         5 KSP Residual norm 2.344964690599e+06 % max 1.367637044108e+00 min 1.464901327469e-03 max/min 9.336035256864e+02
>         6 KSP Residual norm 2.331695060244e+06 % max 1.404943514389e+00 min 1.190280622651e-03 max/min 1.180346455830e+03
>         7 KSP Residual norm 2.271960219657e+06 % max 1.437957455093e+00 min 1.008722431370e-03 max/min 1.425523424853e+03
>         8 KSP Residual norm 2.292028741926e+06 % max 1.502852988492e+00 min 8.809546168835e-04 max/min 1.705936900369e+03
>         9 KSP Residual norm 2.233478095421e+06 % max 1.582008563628e+00 min 7.783319825046e-04 max/min 2.032562709986e+03
>        10 KSP Residual norm 2.217240790630e+06 % max 1.627791394511e+00 min 7.017777386360e-04 max/min 2.319525549035e+03
>        11 KSP Residual norm 2.253686552707e+06 % max 1.659357337462e+00 min 6.359067415045e-04 max/min 2.609435046303e+03
>        12 KSP Residual norm 2.327352703032e+06 % max 1.682006777543e+00 min 5.780023151159e-04 max/min 2.910034672103e+03
>        13 KSP Residual norm 2.258932746968e+06 % max 1.695221701128e+00 min 5.272335154902e-04 max/min 3.215314753940e+03
>        14 KSP Residual norm 2.146539128962e+06 % max 1.701712426981e+00 min 4.879541184491e-04 max/min 3.487443517005e+03
>        15 KSP Residual norm 2.146242364688e+06 % max 1.705375519134e+00 min 4.576872864507e-04 max/min 3.726071423917e+03
>        16 KSP Residual norm 2.160438533108e+06 % max 1.708650293977e+00 min 4.278996767955e-04 max/min 3.993109568984e+03
>        17 KSP Residual norm 2.184700124943e+06 % max 1.710853580610e+00 min 4.021751403604e-04 max/min 4.254001326580e+03
>        18 KSP Residual norm 2.148601462370e+06 % max 1.712408913049e+00 min 3.793690742988e-04 max/min 4.513833701954e+03
>        19 KSP Residual norm 2.195737087965e+06 % max 1.713723267846e+00 min 3.583883046289e-04 max/min 4.781749978199e+03