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

[Denis Davydov]

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