[petsc-users] Unreproducible number of iterations for consecutives solves (GCR + ML)

[Thomas DE-SOZA]

Dear PETSc users,

We've been using the Krylov solvers in PETSc for a while in our software 
package for implicit structural mechanics and recently added algebraic 
multigrid preconditioning through the ML and Hypre libraries provided as 
part of PETSc.
Though we're quite happy with this new feature, we've encountered a 
strange behaviour when using KSPGCR in conjunction with the PCML 
preconditioner. 
Indeed, identical and  consecutives solves inside the same run do not 
display the same number of Krylov iterations even in sequential and we 
were wondering why :

1st solve
723 KSP unpreconditioned resid norm 2.911385065051e-02 true resid norm 
2.911385065051e-02 ||r(i)||/||b|| 9.979426047969e-09

2nd solve
787 KSP unpreconditioned resid norm 2.896035212670e-02 true resid norm 
2.896035212670e-02 ||r(i)||/||b|| 9.926810982197e-09

3rd solve
721 KSP unpreconditioned resid norm 2.913123687343e-02 true resid norm 
2.913123687343e-02 ||r(i)||/||b|| 9.985385566274e-09


Would you say this case requires a great number of iterations and 
therefore reproductibility is not ensured (indeed it is ill-conditioned 
and is not very suited for algebraic multigrid) ?
Or is there a seed somewhere in ML that would explain this ? I searched 
the ML manual for that and couln't find any. We're using the uncoupled 
coarsening scheme in ML (call PetscOptionsSetValue('-pc_ml_CoarsenScheme', 
'Uncoupled', ierr)).

Final notes : several consecutive runs of the program do display identical 
behaviour (that is the 1st solve always require 723 iterations, the 2nd 
787, etc). Moreover other cases that are well-conditioned require the same 
number number of iterations for each consecutive solve (though the 
converged residual differs a bit).

Thanks for any hints,
Thomas
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