[petsc-users] [SLEPc] non-deterministic behaviour in GHEP with Krylov-Schur

[Denis Davydov]

> On 8 Mar 2016, at 11:39, Jose E. Roman <jroman at dsic.upv.es> wrote:
> 
> 
>> El 8 mar 2016, a las 11:28, Denis Davydov <davydden at gmail.com> escribió:
>> 
>> Dear all,
>> 
>> I have some issues with Krylov-Schur applied to GHEP, namely, that different runs on the same machine with the
>> same number of MPI cores gives different eigenvectors results.
>> Here is an example:
>> 
>> mass.InfNorm =15.625
>> stiff.InfNorm=726.549
>> eigenfunction[0].linf=0.459089
>> eigenfunction[1].linf=0.318075
>> eigenfunction[2].linf=0.326199
>> eigenfunction[3].linf=0.312521
>> eigenfunction[4].linf=0.271712
>> eigenfunction[5].linf=0.280744
>> eigenfunction[6].linf=0.315654
>> eigenfunction[7].linf=0.192715
>> eigenfunction[8].linf=0.194826
>> 
>> vs
>> 
>> mass.InfNorm =15.625
>> stiff.InfNorm=726.549
>> eigenfunction[0].linf=0.459089
>> eigenfunction[1].linf=0.329682
>> eigenfunction[2].linf=0.326199
>> eigenfunction[3].linf=0.325289
>> eigenfunction[4].linf=0.284252
>> eigenfunction[5].linf=0.263418
>> eigenfunction[6].linf=0.315756
>> eigenfunction[7].linf=0.194826
>> eigenfunction[8].linf=0.193074
>> 
>> Eigensolver tolerance is absolute and 1e-20. So it’s a bit surprising that there is a quite a big variation in L-inf norm of eigenvectors (0.318075 vs 0.329682).
>> In either case, the biggest issue is non-deterministic behaviour.
>> Is there anything I am missing in Krylov-Schur to make its behaviour as deterministic as possible?
>> 
>> p.s. shift-and-invert is done with LU from MUMPS. Shift value is lower than the exact lowest eigenvalue.
>> 
>> Kind regards,
>> Denis 
>> 
> 
> Which are the eigenvalues?
> 

The eigenvalues are the same for the two runs up to the output precision:

      Eigenvalue 0 : 1.65635
      Eigenvalue 1 : 4.71385
      Eigenvalue 2 : 4.71385
      Eigenvalue 3 : 4.71385
      Eigenvalue 4 : 5.1974
      Eigenvalue 5 : 5.1974
      Eigenvalue 6 : 5.1974
      Eigenvalue 7 : 7.77136
      Eigenvalue 8 : 7.77136