[petsc-users] Neumann BC with non-symmetric matrix

[Jed Brown]

Barry Smith <bsmith at mcs.anl.gov> writes:
>>    4-2) Another observation is that the true residual stagnates way
>>    earlier which I assume is an indication that the RHS is in fact
>>    not in the range of A.
>
>    You can hope this is the case.
>
>    Of course one cannot really know if the residual is stagnating due
>    to an inconsistent right hand side or for some other reason. But if
>    it stagnates at 10^-4 it is probably due to inconsistent right hand
>    side if it stagnates at 10^-12 the right hand side is probably
>    consistent. If it stagnates at 10^-8 then it could be due to
>    inconsistent rhs and or some other reason.

If the true residual stagnates while the preconditioned residual
continues to converge, it may be that the preconditioner is singular or
nearly so.  This often happens if you use a black-box method for a
saddle point problem, for example.
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