[petsc-users] Monotonic convergence in FGMRES.

[Barry Smith]

  Yes but look at the true residual norm it is huge and indicates the residual is not really getting small.

  Barry

On Dec 21, 2010, at 2:26 PM, Vijay S. Mahadevan wrote:

> Barry, I tried with the true_residual_norm option and it gives me the
> exact same convergence as the one I have shown before.
> 
> 45 KSP Residual norm 2.511364148934e-07
>   45 KSP preconditioned resid norm 2.511364148934e-07 true resid norm
> 1.865039278877e+02 ||Ae||/||Ax|| 2.699481989705e+02
>   46 KSP preconditioned resid norm 1.307034672896e-07 true resid norm
> 1.864478183180e+02 ||Ae||/||Ax|| 2.724877015479e+02
> 46 KSP Residual norm 1.307034672896e-07
>   46 KSP preconditioned resid norm 1.307034672896e-07 true resid norm
> 1.864478183180e+02 ||Ae||/||Ax|| 2.724877015479e+02
>   47 KSP preconditioned resid norm 7.105770015635e-08 true resid norm
> 1.864563163311e+02 ||Ae||/||Ax|| 2.722662760395e+02
> 47 KSP Residual norm 7.105770015635e-08
>   47 KSP preconditioned resid norm 7.105770015635e-08 true resid norm
> 1.864563163311e+02 ||Ae||/||Ax|| 2.722662760395e+02
>   48 KSP preconditioned resid norm 4.098578230710e-08 true resid norm
> 1.864560351328e+02 ||Ae||/||Ax|| 2.690284539995e+02
> 48 KSP Residual norm 4.098578230710e-08
>   48 KSP preconditioned resid norm 4.098578230710e-08 true resid norm
> 1.864560351328e+02 ||Ae||/||Ax|| 2.690284539995e+02
>   49 KSP preconditioned resid norm 2.426160176080e-08 true resid norm
> 1.864897210364e+02 ||Ae||/||Ax|| 2.696456942624e+02
> 49 KSP Residual norm 2.426160176080e-08
>   49 KSP preconditioned resid norm 2.426160176080e-08 true resid norm
> 1.864897210364e+02 ||Ae||/||Ax|| 2.696456942624e+02
>   50 KSP preconditioned resid norm 1.864914790828e+02 true resid norm
> 1.864914790828e+02 ||Ae||/||Ax|| 2.798875072987e+02
> 50 KSP Residual norm 1.864914790828e+02
>   50 KSP preconditioned resid norm 1.864914790828e+02 true resid norm
> 1.864914790828e+02 ||Ae||/||Ax|| 2.798875072987e+02
>   51 KSP preconditioned resid norm 6.741080961009e+01 true resid norm
> 6.759768469363e+01 ||Ae||/||Ax|| 1.666964983874e+02
> 51 KSP Residual norm 6.741080961009e+01
>   51 KSP preconditioned resid norm 6.741080961009e+01 true resid norm
> 6.759768469363e+01 ||Ae||/||Ax|| 1.666964983874e+02
>   52 KSP preconditioned resid norm 5.191621875736e+01 true resid norm
> 5.146342142561e+01 ||Ae||/||Ax|| 7.225409161988e+01
> 52 KSP Residual norm 5.191621875736e+01
>   52 KSP preconditioned resid norm 5.191621875736e+01 true resid norm
> 5.146342142561e+01 ||Ae||/||Ax|| 7.225409161988e+01
>   53 KSP preconditioned resid norm 4.513782866249e+01 true resid norm
> 4.546883708687e+01 ||Ae||/||Ax|| 7.426476446334e+01
> 53 KSP Residual norm 4.513782866249e+01
>   53 KSP preconditioned resid norm 4.513782866249e+01 true resid norm
> 4.546883708687e+01 ||Ae||/||Ax|| 7.426476446334e+01
>   54 KSP preconditioned resid norm 3.320195603375e+01 true resid norm
> 3.297361634749e+01 ||Ae||/||Ax|| 5.285029509147e+01
> 
> 
> Vijay
> 
> On Tue, Dec 21, 2010 at 2:23 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>> 
>> On Dec 21, 2010, at 2:08 PM, Jed Brown wrote:
>> 
>>> On Tue, Dec 21, 2010 at 21:04, Barry Smith <bsmith at mcs.anl.gov> wrote:
>>> This is a sign that the preconditioner is seriously messed up and should not be used in its current form.  It can happen if the matrix is nearly singular and for example you use an incomplete factorization for a preconditioner that just screws up the scaling like totally. Run with -ksp_monitor_true_residual and you'll see that the solver is not really solving the problem even though it thinks it is converging fine.
>>> 
>>> FGMRES only does right preconditioning so it should be showing the true residual.
>> 
>>  No because it uses a recursive formula for "computing" the residual norm it does not compute it explicitly. So in extreme circumstances the recursively compute one generates "garbage".
>> 
>>   Barry
>> 
>> 
>>