[petsc-users] Norm_2 calculation

[Matthew Knepley]

On Fri, Jun 5, 2020 at 2:18 PM Fazlul Huq <huq2090 at gmail.com> wrote:

> The same is happening with "-pc_type hypre -pc_hypre_type boomerang" and
> with "-pc_type ilu".
>
> I tried with,
> ierr =
> KSPSetTolerances(ksp,1.e-10,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);CHKERRQ(ierr);
> this also.
>
> Getting higher values of error even then.
>

Always check with

  -pc_type lu

It seems likely that your matrix is flawed.

  Thanks,

     Matt


> Any suggestion to go over this issue?
> Shall I send the code? It's not a large script (single routine, less than
> 100 lines except comment).
>
> Thank you.
> Sincerely,
> Huq
>
> On Fri, Jun 5, 2020 at 12:53 PM Matthew Knepley <knepley at gmail.com> wrote:
>
>> On Fri, Jun 5, 2020 at 12:32 PM Fazlul Huq <huq2090 at gmail.com> wrote:
>>
>>> Input string:
>>> mpiexec -np 1 ./poisson_m -n 10000000 -pc_type cholesky  -ksp_view
>>> -ksp_converged_reason -ksp_monitor_true_residual
>>>
>>> Output is attached herewith.
>>>
>>
>> Solving the problem...
>>
>>   0 KSP preconditioned resid norm 9.741453255800e+07 true resid norm
>> 1.802775638200e+01 ||r(i)||/||b|| 1.000000000000e+00
>>
>>   1 KSP preconditioned resid norm 5.796040438920e+00 true resid norm
>> 3.146946078273e-05 ||r(i)||/||b|| 1.745611606675e-06
>>
>> Your Cholesky preconditioner is crap, probably because the system is
>> either not symmetric or nearly singular. You can see this
>> because the preconditioned residual is 6 orders of magnitude greater than
>> the true residual. Also, if you want to evaluate convergence, you
>> should probably use a lower tolerance like
>>
>>   -ksp_rtol 1e-10
>>
>>   Thanks,
>>
>>      Matt
>>
>> Thank you.
>>> Sincerely,
>>> Huq
>>>
>>> On Fri, Jun 5, 2020 at 10:16 AM Matthew Knepley <knepley at gmail.com>
>>> wrote:
>>>
>>>> On Fri, Jun 5, 2020 at 11:04 AM Fazlul Huq <huq2090 at gmail.com> wrote:
>>>>
>>>>> Hello All,
>>>>> I'm trying to calculate the norm_2 error of a solution.
>>>>> Here, vector s: Analytical solution
>>>>>           vector x: Numerical solution
>>>>>
>>>>> ierr = VecView(s,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
>>>>> ierr = VecView(x,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
>>>>>
>>>>>  ierr = VecAXPY(x,-1.0,s);CHKERRQ(ierr);
>>>>>  ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
>>>>>  ierr = VecView(x,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
>>>>>  ierr = KSPGetIterationNumber(ksp,&its);CHKERRQ(ierr);
>>>>>  if (norm > tol) {
>>>>>     ierr = PetscPrintf(PETSC_COMM_WORLD,"Second Norm of error %g\n",
>>>>> double)norm);CHKERRQ(ierr);
>>>>>     ierr = PetscPrintf(PETSC_COMM_WORLD,"Iterations
>>>>> %D\n",its);CHKERRQ(ierr);
>>>>>   }
>>>>>
>>>>> Am I calculating the "Norm_2" error correctly or making any mistake?
>>>>> Unfortunately, for large sized matrix, say 10^6, I am getting very
>>>>> high value of "Norm_2" error.
>>>>>
>>>>
>>>> 1) I am guessing x comes from a KSPSolve(). It is only as accurate as
>>>> your tolerance
>>>>
>>>> 2) This is the l_2 norm, not the L_2 norm, so if you are using a
>>>> continuum method like FEM, this is likely wrong.
>>>>
>>>>   Thanks,
>>>>
>>>>      Matt
>>>>
>>>>
>>>>> Thank you.
>>>>> Sincerely,
>>>>> Huq
>>>>>
>>>>> --
>>>>>
>>>>> Fazlul Huq
>>>>> Graduate Research Assistant
>>>>> Department of Nuclear, Plasma & Radiological Engineering (NPRE)
>>>>> University of Illinois at Urbana-Champaign (UIUC)
>>>>> E-mail: huq2090 at gmail.com
>>>>>
>>>>
>>>>
>>>> --
>>>> What most experimenters take for granted before they begin their
>>>> experiments is infinitely more interesting than any results to which their
>>>> experiments lead.
>>>> -- Norbert Wiener
>>>>
>>>> https://www.cse.buffalo.edu/~knepley/
>>>> <http://www.cse.buffalo.edu/~knepley/>
>>>>
>>>
>>>
>>> --
>>>
>>> Fazlul Huq
>>> Graduate Research Assistant
>>> Department of Nuclear, Plasma & Radiological Engineering (NPRE)
>>> University of Illinois at Urbana-Champaign (UIUC)
>>> E-mail: huq2090 at gmail.com
>>>
>>
>>
>> --
>> What most experimenters take for granted before they begin their
>> experiments is infinitely more interesting than any results to which their
>> experiments lead.
>> -- Norbert Wiener
>>
>> https://www.cse.buffalo.edu/~knepley/
>> <http://www.cse.buffalo.edu/~knepley/>
>>
>
>
> --
>
> Fazlul Huq
> Graduate Research Assistant
> Department of Nuclear, Plasma & Radiological Engineering (NPRE)
> University of Illinois at Urbana-Champaign (UIUC)
> E-mail: huq2090 at gmail.com
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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