[petsc-users] setting correct tolerances for MG smoother CG at the finest level
Barry Smith
bsmith at petsc.dev
Tue Sep 30 08:27:04 CDT 2025
Would you be able to share your code? I'm at a loss as to why we are seeing this behavior and can much more quickly figure it out by running the code in a debugger.
Barry
You can send the code petsc-maint at mcs.anl.gov <mailto:petsc-maint at mcs.anl.gov> if you don't want to share the code with everyone,
> On Sep 30, 2025, at 5:05 AM, Moral Sanchez, Elena <Elena.Moral.Sanchez at ipp.mpg.de> wrote:
>
> This is what I get:
> Residual norms for mg_levels_1_ solve.
> 0 KSP Residual norm 2.249726733143e+00
> Residual norms for mg_levels_1_ solve.
> 0 KSP unpreconditioned resid norm 2.249726733143e+00 true resid norm 2.249726733143e+00 ||r(i)||/||b|| 1.000000000000e+00
> 1 KSP Residual norm 1.433120400946e+00
> 1 KSP unpreconditioned resid norm 1.433120400946e+00 true resid norm 1.433120400946e+00 ||r(i)||/||b|| 6.370197677051e-01
> 2 KSP Residual norm 1.169262560123e+00
> 2 KSP unpreconditioned resid norm 1.169262560123e+00 true resid norm 1.169262560123e+00 ||r(i)||/||b|| 5.197353718108e-01
> 3 KSP Residual norm 1.323528716607e+00
> 3 KSP unpreconditioned resid norm 1.323528716607e+00 true resid norm 1.323528716607e+00 ||r(i)||/||b|| 5.883064361148e-01
> 4 KSP Residual norm 5.006323254234e-01
> 4 KSP unpreconditioned resid norm 5.006323254234e-01 true resid norm 5.006323254234e-01 ||r(i)||/||b|| 2.225302824775e-01
> 5 KSP Residual norm 3.569836784785e-01
> 5 KSP unpreconditioned resid norm 3.569836784785e-01 true resid norm 3.569836784785e-01 ||r(i)||/||b|| 1.586786844906e-01
> 6 KSP Residual norm 2.493182937513e-01
> 6 KSP unpreconditioned resid norm 2.493182937513e-01 true resid norm 2.493182937513e-01 ||r(i)||/||b|| 1.108215900529e-01
> 7 KSP Residual norm 3.038202502298e-01
> 7 KSP unpreconditioned resid norm 3.038202502298e-01 true resid norm 3.038202502298e-01 ||r(i)||/||b|| 1.350476241198e-01
> 8 KSP Residual norm 2.780214194402e-01
> 8 KSP unpreconditioned resid norm 2.780214194402e-01 true resid norm 2.780214194402e-01 ||r(i)||/||b|| 1.235800843473e-01
> 9 KSP Residual norm 1.676826341491e-01
> 9 KSP unpreconditioned resid norm 1.676826341491e-01 true resid norm 1.676826341491e-01 ||r(i)||/||b|| 7.453466755710e-02
> 10 KSP Residual norm 1.209985378713e-01
> 10 KSP unpreconditioned resid norm 1.209985378713e-01 true resid norm 1.209985378713e-01 ||r(i)||/||b|| 5.378366007245e-02
> 11 KSP Residual norm 9.445076689969e-02
> 11 KSP unpreconditioned resid norm 9.445076689969e-02 true resid norm 9.445076689969e-02 ||r(i)||/||b|| 4.198321756516e-02
> 12 KSP Residual norm 8.308555284580e-02
> 12 KSP unpreconditioned resid norm 8.308555284580e-02 true resid norm 8.308555284580e-02 ||r(i)||/||b|| 3.693139776569e-02
> 13 KSP Residual norm 5.472865592585e-02
> 13 KSP unpreconditioned resid norm 5.472865592585e-02 true resid norm 5.472865592585e-02 ||r(i)||/||b|| 2.432680161532e-02
> 14 KSP Residual norm 4.357870564398e-02
> 14 KSP unpreconditioned resid norm 4.357870564398e-02 true resid norm 4.357870564398e-02 ||r(i)||/||b|| 1.937066622447e-02
> 15 KSP Residual norm 5.079681292439e-02
> 15 KSP unpreconditioned resid norm 5.079681292439e-02 true resid norm 5.079681292439e-02 ||r(i)||/||b|| 2.257910357558e-02
> Linear mg_levels_1_ solve converged due to CONVERGED_ITS iterations 15
> Residual norms for mg_levels_1_ solve.
> 0 KSP Residual norm 5.079681292439e-02
> Residual norms for mg_levels_1_ solve.
> 0 KSP unpreconditioned resid norm 5.079681292439e-02 true resid norm 5.079681292439e-02 ||r(i)||/||b|| 2.257910357559e-02
> 1 KSP Residual norm 2.934938644003e-02
> 1 KSP unpreconditioned resid norm 2.934938644003e-02 true resid norm 2.934938644003e-02 ||r(i)||/||b|| 1.304575618348e-02
> 2 KSP Residual norm 3.257065831294e-02
> 2 KSP unpreconditioned resid norm 3.257065831294e-02 true resid norm 3.257065831294e-02 ||r(i)||/||b|| 1.447760647243e-02
> 3 KSP Residual norm 4.143063876867e-02
> 3 KSP unpreconditioned resid norm 4.143063876867e-02 true resid norm 4.143063876867e-02 ||r(i)||/||b|| 1.841585387164e-02
> 4 KSP Residual norm 4.822471409489e-02
> 4 KSP unpreconditioned resid norm 4.822471409489e-02 true resid norm 4.822471409489e-02 ||r(i)||/||b|| 2.143580968499e-02
> 5 KSP Residual norm 3.197538246153e-02
> 5 KSP unpreconditioned resid norm 3.197538246153e-02 true resid norm 3.197538246153e-02 ||r(i)||/||b|| 1.421300729127e-02
> 6 KSP Residual norm 3.461217019835e-02
> 6 KSP unpreconditioned resid norm 3.461217019835e-02 true resid norm 3.461217019835e-02 ||r(i)||/||b|| 1.538505529958e-02
> 7 KSP Residual norm 3.410193775327e-02
> 7 KSP unpreconditioned resid norm 3.410193775327e-02 true resid norm 3.410193775327e-02 ||r(i)||/||b|| 1.515825777899e-02
> 8 KSP Residual norm 4.690424294464e-02
> 8 KSP unpreconditioned resid norm 4.690424294464e-02 true resid norm 4.690424294464e-02 ||r(i)||/||b|| 2.084886233233e-02
> 9 KSP Residual norm 3.366148892800e-02
> 9 KSP unpreconditioned resid norm 3.366148892800e-02 true resid norm 3.366148892800e-02 ||r(i)||/||b|| 1.496247896783e-02
> 10 KSP Residual norm 4.068015727689e-02
> 10 KSP unpreconditioned resid norm 4.068015727689e-02 true resid norm 4.068015727689e-02 ||r(i)||/||b|| 1.808226602707e-02
> 11 KSP Residual norm 2.658836123104e-02
> 11 KSP unpreconditioned resid norm 2.658836123104e-02 true resid norm 2.658836123104e-02 ||r(i)||/||b|| 1.181848481389e-02
> 12 KSP Residual norm 2.826244186003e-02
> 12 KSP unpreconditioned resid norm 2.826244186003e-02 true resid norm 2.826244186003e-02 ||r(i)||/||b|| 1.256261102456e-02
> 13 KSP Residual norm 2.981793619508e-02
> 13 KSP unpreconditioned resid norm 2.981793619508e-02 true resid norm 2.981793619508e-02 ||r(i)||/||b|| 1.325402581380e-02
> 14 KSP Residual norm 3.525455091450e-02
> 14 KSP unpreconditioned resid norm 3.525455091450e-02 true resid norm 3.525455091450e-02 ||r(i)||/||b|| 1.567059251914e-02
> 15 KSP Residual norm 2.331539121838e-02
> 15 KSP unpreconditioned resid norm 2.331539121838e-02 true resid norm 2.331539121838e-02 ||r(i)||/||b|| 1.036365478300e-02
> Linear mg_levels_1_ solve converged due to CONVERGED_ITS iterations 15
> Residual norms for mg_levels_1_ solve.
> 0 KSP Residual norm 2.421498365806e-02
> Residual norms for mg_levels_1_ solve.
> 0 KSP unpreconditioned resid norm 2.421498365806e-02 true resid norm 2.421498365806e-02 ||r(i)||/||b|| 1.000000000000e+00
> 1 KSP Residual norm 1.761072112362e-02
> 1 KSP unpreconditioned resid norm 1.761072112362e-02 true resid norm 1.761072112362e-02 ||r(i)||/||b|| 7.272654556492e-01
> 2 KSP Residual norm 1.400842489042e-02
> 2 KSP unpreconditioned resid norm 1.400842489042e-02 true resid norm 1.400842489042e-02 ||r(i)||/||b|| 5.785023474818e-01
> 3 KSP Residual norm 1.419665483348e-02
> 3 KSP unpreconditioned resid norm 1.419665483348e-02 true resid norm 1.419665483348e-02 ||r(i)||/||b|| 5.862756314004e-01
> 4 KSP Residual norm 1.617590701667e-02
> 4 KSP unpreconditioned resid norm 1.617590701667e-02 true resid norm 1.617590701667e-02 ||r(i)||/||b|| 6.680123036665e-01
> 5 KSP Residual norm 1.354824081005e-02
> 5 KSP unpreconditioned resid norm 1.354824081005e-02 true resid norm 1.354824081005e-02 ||r(i)||/||b|| 5.594982429624e-01
> 6 KSP Residual norm 1.387252917475e-02
> 6 KSP unpreconditioned resid norm 1.387252917475e-02 true resid norm 1.387252917475e-02 ||r(i)||/||b|| 5.728902967950e-01
> 7 KSP Residual norm 1.514043102087e-02
> 7 KSP unpreconditioned resid norm 1.514043102087e-02 true resid norm 1.514043102087e-02 ||r(i)||/||b|| 6.252505157414e-01
> 8 KSP Residual norm 1.275811124745e-02
> 8 KSP unpreconditioned resid norm 1.275811124745e-02 true resid norm 1.275811124745e-02 ||r(i)||/||b|| 5.268684640721e-01
> 9 KSP Residual norm 1.241039155981e-02
> 9 KSP unpreconditioned resid norm 1.241039155981e-02 true resid norm 1.241039155981e-02 ||r(i)||/||b|| 5.125087728764e-01
> 10 KSP Residual norm 9.585207801652e-03
> 10 KSP unpreconditioned resid norm 9.585207801652e-03 true resid norm 9.585207801652e-03 ||r(i)||/||b|| 3.958378802565e-01
> 11 KSP Residual norm 9.022641230732e-03
> 11 KSP unpreconditioned resid norm 9.022641230732e-03 true resid norm 9.022641230732e-03 ||r(i)||/||b|| 3.726057121550e-01
> 12 KSP Residual norm 1.187709152046e-02
> 12 KSP unpreconditioned resid norm 1.187709152046e-02 true resid norm 1.187709152046e-02 ||r(i)||/||b|| 4.904852172597e-01
> 13 KSP Residual norm 1.084880112494e-02
> 13 KSP unpreconditioned resid norm 1.084880112494e-02 true resid norm 1.084880112494e-02 ||r(i)||/||b|| 4.480201712351e-01
> 14 KSP Residual norm 8.194750346781e-03
> 14 KSP unpreconditioned resid norm 8.194750346781e-03 true resid norm 8.194750346781e-03 ||r(i)||/||b|| 3.384165136140e-01
> 15 KSP Residual norm 7.614246199165e-03
> 15 KSP unpreconditioned resid norm 7.614246199165e-03 true resid norm 7.614246199165e-03 ||r(i)||/||b|| 3.144435819857e-01
> Linear mg_levels_1_ solve converged due to CONVERGED_ITS iterations 15
> Residual norms for mg_levels_1_ solve.
> 0 KSP Residual norm 7.614246199165e-03
> Residual norms for mg_levels_1_ solve.
> 0 KSP unpreconditioned resid norm 7.614246199165e-03 true resid norm 7.614246199165e-03 ||r(i)||/||b|| 3.144435819857e-01
> 1 KSP Residual norm 5.620014684145e-03
> 1 KSP unpreconditioned resid norm 5.620014684145e-03 true resid norm 5.620014684145e-03 ||r(i)||/||b|| 2.320883120759e-01
> 2 KSP Residual norm 6.643368363907e-03
> 2 KSP unpreconditioned resid norm 6.643368363907e-03 true resid norm 6.643368363907e-03 ||r(i)||/||b|| 2.743494878096e-01
> 3 KSP Residual norm 8.708642393659e-03
> 3 KSP unpreconditioned resid norm 8.708642393659e-03 true resid norm 8.708642393659e-03 ||r(i)||/||b|| 3.596385823189e-01
> 4 KSP Residual norm 6.401852907459e-03
> 4 KSP unpreconditioned resid norm 6.401852907459e-03 true resid norm 6.401852907459e-03 ||r(i)||/||b|| 2.643756856440e-01
> 5 KSP Residual norm 7.230576215262e-03
> 5 KSP unpreconditioned resid norm 7.230576215262e-03 true resid norm 7.230576215262e-03 ||r(i)||/||b|| 2.985992605803e-01
> 6 KSP Residual norm 6.204081601285e-03
> 6 KSP unpreconditioned resid norm 6.204081601285e-03 true resid norm 6.204081601285e-03 ||r(i)||/||b|| 2.562083744880e-01
> 7 KSP Residual norm 7.038656665944e-03
> 7 KSP unpreconditioned resid norm 7.038656665944e-03 true resid norm 7.038656665944e-03 ||r(i)||/||b|| 2.906736079337e-01
> 8 KSP Residual norm 7.194079694050e-03
> 8 KSP unpreconditioned resid norm 7.194079694050e-03 true resid norm 7.194079694050e-03 ||r(i)||/||b|| 2.970920730585e-01
> 9 KSP Residual norm 6.353576889135e-03
> 9 KSP unpreconditioned resid norm 6.353576889135e-03 true resid norm 6.353576889135e-03 ||r(i)||/||b|| 2.623820432363e-01
> 10 KSP Residual norm 7.313589502731e-03
> 10 KSP unpreconditioned resid norm 7.313589502731e-03 true resid norm 7.313589502731e-03 ||r(i)||/||b|| 3.020274391264e-01
> 11 KSP Residual norm 6.643320423193e-03
> 11 KSP unpreconditioned resid norm 6.643320423193e-03 true resid norm 6.643320423193e-03 ||r(i)||/||b|| 2.743475080142e-01
> 12 KSP Residual norm 7.235443182108e-03
> 12 KSP unpreconditioned resid norm 7.235443182108e-03 true resid norm 7.235443182108e-03 ||r(i)||/||b|| 2.988002504681e-01
> 13 KSP Residual norm 4.971292307201e-03
> 13 KSP unpreconditioned resid norm 4.971292307201e-03 true resid norm 4.971292307201e-03 ||r(i)||/||b|| 2.052981896416e-01
> 14 KSP Residual norm 5.357933842147e-03
> 14 KSP unpreconditioned resid norm 5.357933842147e-03 true resid norm 5.357933842147e-03 ||r(i)||/||b|| 2.212652264320e-01
> 15 KSP Residual norm 5.841682994497e-03
> 15 KSP unpreconditioned resid norm 5.841682994497e-03 true resid norm 5.841682994497e-03 ||r(i)||/||b|| 2.412424917146e-01
> Linear mg_levels_1_ solve converged due to CONVERGED_ITS iterations 15
> Cheers,
> Elena
> From: Barry Smith <bsmith at petsc.dev <mailto:bsmith at petsc.dev>>
> Sent: 29 September 2025 20:31:26
> To: Moral Sanchez, Elena
> Cc: Mark Adams; petsc-users
> Subject: Re: [petsc-users] setting correct tolerances for MG smoother CG at the finest level
>
>
> Thanks. I missed something earlier in the KSPView
>
>>> using UNPRECONDITIONED norm type for convergence test
>
> Please add the options
>
>>>>> -ksp_monitor_true_residual -mg_levels_ksp_monitor_true_residual
>
> It is using the unpreconditioned residual norms for convergence testing but we are printing the preconditioned norms.
>
> Barry
>
>
>> On Sep 29, 2025, at 11:12 AM, Moral Sanchez, Elena <Elena.Moral.Sanchez at ipp.mpg.de <mailto:Elena.Moral.Sanchez at ipp.mpg.de>> wrote:
>>
>> This is the output:
>> Residual norms for mg_levels_1_ solve.
>> 0 KSP Residual norm 2.249726733143e+00
>> 1 KSP Residual norm 1.433120400946e+00
>> 2 KSP Residual norm 1.169262560123e+00
>> 3 KSP Residual norm 1.323528716607e+00
>> 4 KSP Residual norm 5.006323254234e-01
>> 5 KSP Residual norm 3.569836784785e-01
>> 6 KSP Residual norm 2.493182937513e-01
>> 7 KSP Residual norm 3.038202502298e-01
>> 8 KSP Residual norm 2.780214194402e-01
>> 9 KSP Residual norm 1.676826341491e-01
>> 10 KSP Residual norm 1.209985378713e-01
>> 11 KSP Residual norm 9.445076689969e-02
>> 12 KSP Residual norm 8.308555284580e-02
>> 13 KSP Residual norm 5.472865592585e-02
>> 14 KSP Residual norm 4.357870564398e-02
>> 15 KSP Residual norm 5.079681292439e-02
>> Linear mg_levels_1_ solve converged due to CONVERGED_ITS iterations 15
>> Residual norms for mg_levels_1_ solve.
>> 0 KSP Residual norm 5.079681292439e-02
>> 1 KSP Residual norm 2.934938644003e-02
>> 2 KSP Residual norm 3.257065831294e-02
>> 3 KSP Residual norm 4.143063876867e-02
>> 4 KSP Residual norm 4.822471409489e-02
>> 5 KSP Residual norm 3.197538246153e-02
>> 6 KSP Residual norm 3.461217019835e-02
>> 7 KSP Residual norm 3.410193775327e-02
>> 8 KSP Residual norm 4.690424294464e-02
>> 9 KSP Residual norm 3.366148892800e-02
>> 10 KSP Residual norm 4.068015727689e-02
>> 11 KSP Residual norm 2.658836123104e-02
>> 12 KSP Residual norm 2.826244186003e-02
>> 13 KSP Residual norm 2.981793619508e-02
>> 14 KSP Residual norm 3.525455091450e-02
>> 15 KSP Residual norm 2.331539121838e-02
>> Linear mg_levels_1_ solve converged due to CONVERGED_ITS iterations 15
>> Residual norms for mg_levels_1_ solve.
>> 0 KSP Residual norm 2.421498365806e-02
>> 1 KSP Residual norm 1.761072112362e-02
>> 2 KSP Residual norm 1.400842489042e-02
>> 3 KSP Residual norm 1.419665483348e-02
>> 4 KSP Residual norm 1.617590701667e-02
>> 5 KSP Residual norm 1.354824081005e-02
>> 6 KSP Residual norm 1.387252917475e-02
>> 7 KSP Residual norm 1.514043102087e-02
>> 8 KSP Residual norm 1.275811124745e-02
>> 9 KSP Residual norm 1.241039155981e-02
>> 10 KSP Residual norm 9.585207801652e-03
>> 11 KSP Residual norm 9.022641230732e-03
>> 12 KSP Residual norm 1.187709152046e-02
>> 13 KSP Residual norm 1.084880112494e-02
>> 14 KSP Residual norm 8.194750346781e-03
>> 15 KSP Residual norm 7.614246199165e-03
>> Linear mg_levels_1_ solve converged due to CONVERGED_ITS iterations 15
>> Residual norms for mg_levels_1_ solve.
>> 0 KSP Residual norm 7.614246199165e-03
>> 1 KSP Residual norm 5.620014684145e-03
>> 2 KSP Residual norm 6.643368363907e-03
>> 3 KSP Residual norm 8.708642393659e-03
>> 4 KSP Residual norm 6.401852907459e-03
>> 5 KSP Residual norm 7.230576215262e-03
>> 6 KSP Residual norm 6.204081601285e-03
>> 7 KSP Residual norm 7.038656665944e-03
>> 8 KSP Residual norm 7.194079694050e-03
>> 9 KSP Residual norm 6.353576889135e-03
>> 10 KSP Residual norm 7.313589502731e-03
>> 11 KSP Residual norm 6.643320423193e-03
>> 12 KSP Residual norm 7.235443182108e-03
>> 13 KSP Residual norm 4.971292307201e-03
>> 14 KSP Residual norm 5.357933842147e-03
>> 15 KSP Residual norm 5.841682994497e-03
>> Linear mg_levels_1_ solve converged due to CONVERGED_ITS iterations 15
>>
>> From: Barry Smith <bsmith at petsc.dev <mailto:bsmith at petsc.dev>>
>> Sent: 29 September 2025 15:56:33
>> To: Moral Sanchez, Elena
>> Cc: Mark Adams; petsc-users
>> Subject: Re: [petsc-users] setting correct tolerances for MG smoother CG at the finest level
>>
>>
>> I asked you to run with
>>
>>>>> -ksp_monitor -mg_levels_ksp_monitor -ksp_converged_reason -mg_levels_ksp_converged_reason
>>
>> you chose not to, delaying the process of understanding what is happening.
>>
>> Please run with those options and send the output. My guess is that you are computing the "residual norms" in your own monitor code, and it is doing so differently than what PETSc does, thus resulting in the appearance of a sufficiently small residual norm, whereas PETSc may not have calculated something that small.
>>
>> Barry
>>
>>
>>> On Sep 29, 2025, at 8:39 AM, Moral Sanchez, Elena <Elena.Moral.Sanchez at ipp.mpg.de <mailto:Elena.Moral.Sanchez at ipp.mpg.de>> wrote:
>>>
>>> Thanks for the hint. I agree that the coarse solve should be much more "accurate". However, for the moment I am just trying to understand what the MG is doing exactly.
>>>
>>> I am puzzled to see that the fine grid smoother ("lvl 0") does not stop when the residual becomes less than 1e-1. It should converge due to the atol.
>>>
>>> From: Mark Adams <mfadams at lbl.gov <mailto:mfadams at lbl.gov>>
>>> Sent: 29 September 2025 14:20:56
>>> To: Moral Sanchez, Elena
>>> Cc: Barry Smith; petsc-users
>>> Subject: Re: [petsc-users] setting correct tolerances for MG smoother CG at the finest level
>>>
>>> Oh I see the coarse grid solver in your full solver output now.
>>> You still want an accurate coarse grid solve. Usually (the default in GAMG) you use a direct solver on one process, and cousin until the coarse grid is small enough to make that cheap.
>>>
>>> On Mon, Sep 29, 2025 at 8:07 AM Moral Sanchez, Elena <Elena.Moral.Sanchez at ipp.mpg.de <mailto:Elena.Moral.Sanchez at ipp.mpg.de>> wrote:
>>>> Hi, I doubled the system size and changed the tolerances just to show a better example of the problem. This is the output of the callbacks in the first iteration:
>>>> CG Iter 0/1 | res = 2.25e+00/1.00e-09 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 0/15 | res = 2.25e+00/1.00e-01 | 0.3 s
>>>> MG lvl 0 (s=884): CG Iter 1/15 | res = 1.43e+00/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 2/15 | res = 1.17e+00/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 3/15 | res = 1.32e+00/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 4/15 | res = 5.01e-01/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 5/15 | res = 3.57e-01/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 6/15 | res = 2.49e-01/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 7/15 | res = 3.04e-01/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 8/15 | res = 2.78e-01/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 9/15 | res = 1.68e-01/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 10/15 | res = 1.21e-01/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 11/15 | res = 9.45e-02/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 12/15 | res = 8.31e-02/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 13/15 | res = 5.47e-02/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 14/15 | res = 4.36e-02/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 15/15 | res = 5.08e-02/1.00e-01 | 0.1 s
>>>> ConvergedReason MG lvl 0: 4
>>>> MG lvl -1 (s=524): CG Iter 0/15 | res = 8.15e-02/1.00e-01 | 3.0 s
>>>> ConvergedReason MG lvl -1: 3
>>>> MG lvl 0 (s=884): CG Iter 0/15 | res = 5.08e-02/1.00e-01 | 0.3 s
>>>> MG lvl 0 (s=884): CG Iter 1/15 | res = 2.93e-02/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 2/15 | res = 3.26e-02/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 3/15 | res = 4.14e-02/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 4/15 | res = 4.82e-02/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 5/15 | res = 3.20e-02/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 6/15 | res = 3.46e-02/1.00e-01 | 0.3 s
>>>> MG lvl 0 (s=884): CG Iter 7/15 | res = 3.41e-02/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 8/15 | res = 4.69e-02/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 9/15 | res = 3.37e-02/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 10/15 | res = 4.07e-02/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 11/15 | res = 2.66e-02/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 12/15 | res = 2.83e-02/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 13/15 | res = 2.98e-02/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 14/15 | res = 3.53e-02/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 15/15 | res = 2.33e-02/1.00e-01 | 0.2 s
>>>> ConvergedReason MG lvl 0: 4
>>>> CG Iter 1/1 | res = 2.42e-02/1.00e-09 | 5.6 s
>>>> MG lvl 0 (s=884): CG Iter 0/15 | res = 2.42e-02/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 1/15 | res = 1.76e-02/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 2/15 | res = 1.40e-02/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 3/15 | res = 1.42e-02/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 4/15 | res = 1.62e-02/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 5/15 | res = 1.35e-02/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 6/15 | res = 1.39e-02/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 7/15 | res = 1.51e-02/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 8/15 | res = 1.28e-02/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 9/15 | res = 1.24e-02/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 10/15 | res = 9.59e-03/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 11/15 | res = 9.02e-03/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 12/15 | res = 1.19e-02/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 13/15 | res = 1.08e-02/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 14/15 | res = 8.19e-03/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 15/15 | res = 7.61e-03/1.00e-01 | 0.1 s
>>>> ConvergedReason MG lvl 0: 4
>>>> MG lvl -1 (s=524): CG Iter 0/15 | res = 1.38e-02/1.00e-01 | 5.2 s
>>>> ConvergedReason MG lvl -1: 3
>>>> MG lvl 0 (s=884): CG Iter 0/15 | res = 7.61e-03/1.00e-01 | 0.2 s
>>>> MG lvl 0 (s=884): CG Iter 1/15 | res = 5.62e-03/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 2/15 | res = 6.64e-03/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 3/15 | res = 8.71e-03/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 4/15 | res = 6.40e-03/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 5/15 | res = 7.23e-03/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 6/15 | res = 6.20e-03/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 7/15 | res = 7.04e-03/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 8/15 | res = 7.19e-03/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 9/15 | res = 6.35e-03/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 10/15 | res = 7.31e-03/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 11/15 | res = 6.64e-03/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 12/15 | res = 7.24e-03/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 13/15 | res = 4.97e-03/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 14/15 | res = 5.36e-03/1.00e-01 | 0.1 s
>>>> MG lvl 0 (s=884): CG Iter 15/15 | res = 5.84e-03/1.00e-01 | 0.1 s
>>>> ConvergedReason MG lvl 0: 4
>>>> CG ConvergedReason: -3
>>>>
>>>> For completeness, I add here the -ksp_view of the whole solver:
>>>> KSP Object: 1 MPI process
>>>> type: cg
>>>> variant HERMITIAN
>>>> maximum iterations=1, nonzero initial guess
>>>> tolerances: relative=1e-08, absolute=1e-09, divergence=10000.
>>>> left preconditioning
>>>> using UNPRECONDITIONED norm type for convergence test
>>>> PC Object: 1 MPI process
>>>> type: mg
>>>> type is MULTIPLICATIVE, levels=2 cycles=v
>>>> Cycles per PCApply=1
>>>> Not using Galerkin computed coarse grid matrices
>>>> Coarse grid solver -- level 0 -------------------------------
>>>> KSP Object: (mg_coarse_) 1 MPI process
>>>> type: cg
>>>> variant HERMITIAN
>>>> maximum iterations=15, nonzero initial guess
>>>> tolerances: relative=0.1, absolute=0.1, divergence=1e+30
>>>> left preconditioning
>>>> using UNPRECONDITIONED norm type for convergence test
>>>> PC Object: (mg_coarse_) 1 MPI process
>>>> type: none
>>>> linear system matrix = precond matrix:
>>>> Mat Object: 1 MPI process
>>>> type: python
>>>> rows=524, cols=524
>>>> Python: Solver_petsc.LeastSquaresOperator
>>>> Down solver (pre-smoother) on level 1 -------------------------------
>>>> KSP Object: (mg_levels_1_) 1 MPI process
>>>> type: cg
>>>> variant HERMITIAN
>>>> maximum iterations=15, nonzero initial guess
>>>> tolerances: relative=0.1, absolute=0.1, divergence=1e+30
>>>> left preconditioning
>>>> using UNPRECONDITIONED norm type for convergence test
>>>> PC Object: (mg_levels_1_) 1 MPI process
>>>> type: none
>>>> linear system matrix = precond matrix:
>>>> Mat Object: 1 MPI process
>>>> type: python
>>>> rows=884, cols=884
>>>> Python: Solver_petsc.LeastSquaresOperator
>>>> Up solver (post-smoother) same as down solver (pre-smoother)
>>>> linear system matrix = precond matrix:
>>>> Mat Object: 1 MPI process
>>>> type: python
>>>> rows=884, cols=884
>>>> Python: Solver_petsc.LeastSquaresOperator
>>>>
>>>> Regarding Mark's Email: What do you mean with "the whole solver doesn't have a coarse grid"? I am using my own Restriction and Interpolation operators.
>>>> Thanks for the help,
>>>> Elena
>>>>
>>>> From: Mark Adams <mfadams at lbl.gov <mailto:mfadams at lbl.gov>>
>>>> Sent: 28 September 2025 20:13:54
>>>> To: Barry Smith
>>>> Cc: Moral Sanchez, Elena; petsc-users
>>>> Subject: Re: [petsc-users] setting correct tolerances for MG smoother CG at the finest level
>>>>
>>>> Not sure why your "whole"solver does not have a coarse grid but this is wrong:
>>>>
>>>>> KSP Object: (mg_coarse_) 1 MPI process
>>>>> type: cg
>>>>> variant HERMITIAN
>>>>> maximum iterations=100, initial guess is zero
>>>>> tolerances: relative=0.1, absolute=0.1, divergence=1e+30
>>>>>
>>>>> The coarse grid has to be accurate. The defaults are a good place to start: max_it=10.000, rtol=1e-5, atol=1e-30 (ish)
>>>>
>>>> On Fri, Sep 26, 2025 at 3:21 PM Barry Smith <bsmith at petsc.dev <mailto:bsmith at petsc.dev>> wrote:
>>>>> Looks reasonable. Send the output running with
>>>>>
>>>>> -ksp_monitor -mg_levels_ksp_monitor -ksp_converged_reason -mg_levels_ksp_converged_reason
>>>>>
>>>>>> On Sep 26, 2025, at 1:19 PM, Moral Sanchez, Elena <Elena.Moral.Sanchez at ipp.mpg.de <mailto:Elena.Moral.Sanchez at ipp.mpg.de>> wrote:
>>>>>>
>>>>>> Dear Barry,
>>>>>>
>>>>>> This is -ksp_view for the smoother at the finest level:
>>>>>> KSP Object: (mg_levels_1_) 1 MPI process
>>>>>> type: cg
>>>>>> variant HERMITIAN
>>>>>> maximum iterations=10, nonzero initial guess
>>>>>> tolerances: relative=0.1, absolute=0.1, divergence=1e+30
>>>>>> left preconditioning
>>>>>> using UNPRECONDITIONED norm type for convergence test
>>>>>> PC Object: (mg_levels_1_) 1 MPI process
>>>>>> type: none
>>>>>> linear system matrix = precond matrix:
>>>>>> Mat Object: 1 MPI process
>>>>>> type: python
>>>>>> rows=524, cols=524
>>>>>> Python: Solver_petsc.LeastSquaresOperator
>>>>>> And at the coarsest level:
>>>>>> KSP Object: (mg_coarse_) 1 MPI process
>>>>>> type: cg
>>>>>> variant HERMITIAN
>>>>>> maximum iterations=100, initial guess is zero
>>>>>> tolerances: relative=0.1, absolute=0.1, divergence=1e+30
>>>>>> left preconditioning
>>>>>> using UNPRECONDITIONED norm type for convergence test
>>>>>> PC Object: (mg_coarse_) 1 MPI process
>>>>>> type: none
>>>>>> linear system matrix = precond matrix:
>>>>>> Mat Object: 1 MPI process
>>>>>> type: python
>>>>>> rows=344, cols=344
>>>>>> Python: Solver_petsc.LeastSquaresOperator
>>>>>> And for the whole solver:
>>>>>> KSP Object: 1 MPI process
>>>>>> type: cg
>>>>>> variant HERMITIAN
>>>>>> maximum iterations=100, nonzero initial guess
>>>>>> tolerances: relative=1e-08, absolute=1e-09, divergence=10000.
>>>>>> left preconditioning
>>>>>> using UNPRECONDITIONED norm type for convergence test
>>>>>> PC Object: 1 MPI process
>>>>>> type: mg
>>>>>> type is MULTIPLICATIVE, levels=2 cycles=v
>>>>>> Cycles per PCApply=1
>>>>>> Not using Galerkin computed coarse grid matrices
>>>>>> Coarse grid solver -- level 0 -------------------------------
>>>>>> KSP Object: (mg_coarse_) 1 MPI process
>>>>>> type: cg
>>>>>> variant HERMITIAN
>>>>>> maximum iterations=100, initial guess is zero
>>>>>> tolerances: relative=0.1, absolute=0.1, divergence=1e+30
>>>>>> left preconditioning
>>>>>> using UNPRECONDITIONED norm type for convergence test
>>>>>> PC Object: (mg_coarse_) 1 MPI process
>>>>>> type: none
>>>>>> linear system matrix = precond matrix:
>>>>>> Mat Object: 1 MPI process
>>>>>> type: python
>>>>>> rows=344, cols=344
>>>>>> Python: Solver_petsc.LeastSquaresOperator
>>>>>> Down solver (pre-smoother) on level 1 -------------------------------
>>>>>> KSP Object: (mg_levels_1_) 1 MPI process
>>>>>> type: cg
>>>>>> variant HERMITIAN
>>>>>> maximum iterations=10, nonzero initial guess
>>>>>> tolerances: relative=0.1, absolute=0.1, divergence=1e+30
>>>>>> left preconditioning
>>>>>> using UNPRECONDITIONED norm type for convergence test
>>>>>> PC Object: (mg_levels_1_) 1 MPI process
>>>>>> type: none
>>>>>> linear system matrix = precond matrix:
>>>>>> Mat Object: 1 MPI process
>>>>>> type: python
>>>>>> rows=524, cols=524
>>>>>> Python: Solver_petsc.LeastSquaresOperator
>>>>>> Up solver (post-smoother) same as down solver (pre-smoother)
>>>>>> linear system matrix = precond matrix:
>>>>>> Mat Object: 1 MPI process
>>>>>> type: python
>>>>>> rows=524, cols=524
>>>>>> Python: Solver_petsc.LeastSquaresOperator
>>>>>> Best,
>>>>>> Elena
>>>>>>
>>>>>>
>>>>>> From: Barry Smith <bsmith at petsc.dev <mailto:bsmith at petsc.dev>>
>>>>>> Sent: 26 September 2025 19:05:02
>>>>>> To: Moral Sanchez, Elena
>>>>>> Cc: petsc-users at mcs.anl.gov <mailto:petsc-users at mcs.anl.gov>
>>>>>> Subject: Re: [petsc-users] setting correct tolerances for MG smoother CG at the finest level
>>>>>>
>>>>>>
>>>>>> Send the output using -ksp_view
>>>>>>
>>>>>> Normally one uses a fixed number of iterations of smoothing on level with multigrid rather than a tolerance, but yes PETSc should respect such a tolerance.
>>>>>>
>>>>>> Barry
>>>>>>
>>>>>>
>>>>>>> On Sep 26, 2025, at 12:49 PM, Moral Sanchez, Elena <Elena.Moral.Sanchez at ipp.mpg.de <mailto:Elena.Moral.Sanchez at ipp.mpg.de>> wrote:
>>>>>>>
>>>>>>> Hi,
>>>>>>> I am using multigrid (multiplicative) as a preconditioner with a V-cycle of two levels. At each level, I am setting CG as the smoother with certain tolerance.
>>>>>>>
>>>>>>> What I observe is that in the finest level the CG continues iterating after the residual norm reaches the tolerance (atol) and it only stops when reaching the maximum number of iterations at that level. At the coarsest level this does not occur and the CG stops when the tolerance is reached.
>>>>>>>
>>>>>>> I double-checked that the smoother at the finest level has the right tolerance. And I am using a Monitor function to track the residual.
>>>>>>>
>>>>>>> Do you know how to make the smoother at the finest level stop when reaching the tolerance?
>>>>>>>
>>>>>>> Cheers,
>>>>>>> Elena.
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