[petsc-users] Increasing norm with finer mesh

Mon Oct 8 17:58:05 CDT 2018

And what is the x-axis? And what solver (preconditioner) are you using w/o
LU (2nd graph)?

On Mon, Oct 8, 2018 at 6:47 PM Matthew Knepley <knepley at gmail.com> wrote:

> On Mon, Oct 8, 2018 at 6:13 PM Weizhuo Wang <weizhuo2 at illinois.edu> wrote:
>
>> Sorry I was caught up with midterms for the last few days. I tried the lu
>> decomposition today and the 2-norm is pretty stable at ~ 10^-15, which is
>> expected for double precision. Since the discretization error is so small,
>> it would be reasonable to assume the rest is majority the algebraic error.
>>
>
> What are you plotting? It looks like only the algebraic error or residual.
> There is absolutely no way your discretization error is 1e-14.
>
>   Thanks,
>
>     Matt
>
>
>> Then looking at the result without the -pc_type lu flag(second graph),
>> the error is asymptoting to a constant several magnitudes larger than the
>> tolerance set for the solver. (atol=1e-12, rtol=1e-9) Is this the expected
>> behavior? Shouldn't it decrease with finer grid?
>> [image: LU.png]
>> [image: Total.png]
>>
>> On Tue, Oct 2, 2018 at 6:52 PM Matthew Knepley <knepley at gmail.com> wrote:
>>
>>> On Tue, Oct 2, 2018 at 5:26 PM Weizhuo Wang <weizhuo2 at illinois.edu>
>>> wrote:
>>>
>>>> I didn't specify a tolerance, it was using the default tolerance.
>>>> Doesn't the asymptoting norm implies finer grid won't help to get finer
>>>> solution?
>>>>
>>>
>>> There are two things going on in your test, discretization error
>>> controlled by the grid, and algebraic error controlled by the solver. This
>>> makes it difficult to isolate what is happening. However, it seems clear
>>> that your plot is looking at algebraic error. You can confirm this by using
>>>
>>>   -pc_type lu
>>>
>>> for the solve. Then all you have is discretization error.
>>>
>>>   Thanks,
>>>
>>>      Matt
>>>
>>>
>>>> Mark Adams <mfadams at lbl.gov> ：
>>>>
>>>>>
>>>>>
>>>>> On Tue, Oct 2, 2018 at 5:04 PM Weizhuo Wang <weizhuo2 at illinois.edu>
>>>>> wrote:
>>>>>
>>>>>> Yes I was using one norm in my Helmholtz code, the example code used
>>>>>> 2 norm. But now I am using 2 norm in both code.
>>>>>>
>>>>>>   /*
>>>>>>      Check the error
>>>>>>   */
>>>>>>   ierr = VecAXPY(x,-1.0,u); CHKERRQ(ierr);
>>>>>>   ierr = VecNorm(x,NORM_1,&norm); CHKERRQ(ierr);
>>>>>>   ierr = KSPGetIterationNumber(ksp,&its); CHKERRQ(ierr);
>>>>>>   ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations
>>>>>> %D\n",(double)norm/(m*n),its); CHKERRQ(ierr);
>>>>>>
>>>>>>  I made a plot to show the increase:
>>>>>>
>>>>>
>>>>>
>>>>> FYI, this is asymptoting to a constant.  What solver tolerance are
>>>>> you using?
>>>>>
>>>>>
>>>>>>
>>>>>> [image: Norm comparison.png]
>>>>>>
>>>>>> Mark Adams <mfadams at lbl.gov>：
>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> On Tue, Oct 2, 2018 at 2:24 PM Weizhuo Wang <weizhuo2 at illinois.edu>
>>>>>>> wrote:
>>>>>>>
>>>>>>>> The example code and makefile are attached below. The whole thing
>>>>>>>> started as I tried to build a Helmholtz solver, and the mean error
>>>>>>>> (calculated by: sum( | numerical_sol - analytical_sol | / analytical_sol )
>>>>>>>> )
>>>>>>>>
>>>>>>>
>>>>>>> This is a one norm. If you use max (instead of sum) then you don't
>>>>>>> need to scale. You do have to be careful about dividing by (near) zero.
>>>>>>>
>>>>>>>
>>>>>>>> increases as I use finer and finer grids.
>>>>>>>>
>>>>>>>
>>>>>>> What was the rate of increase?
>>>>>>>
>>>>>>>
>>>>>>>> Then I looked at the example 12 (Laplacian solver) which is similar
>>>>>>>> to what I did to see if I have missed something. The example is using
>>>>>>>> 2_norm. I have made some minor modifications (3 places) on the code, you
>>>>>>>> can search 'Modified' in the code to see them.
>>>>>>>>
>>>>>>>> If this helps: I configured the PETSc to use real and double
>>>>>>>> precision. Changed the name of the example code from ex12.c to ex12c.c
>>>>>>>>
>>>>>>>> Thanks for all your reply!
>>>>>>>>
>>>>>>>> Weizhuo
>>>>>>>>
>>>>>>>>
>>>>>>>> Smith, Barry F. <bsmith at mcs.anl.gov>
>>>>>>>>
>>>>>>>>
>>>>>>>>>    Please send your version of the example that computes the mean
>>>>>>>>> norm of the grid; I suspect we are talking apples and oranges
>>>>>>>>>
>>>>>>>>>    Barry
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> > On Oct 1, 2018, at 7:51 PM, Weizhuo Wang <weizhuo2 at illinois.edu>
>>>>>>>>> wrote:
>>>>>>>>> >
>>>>>>>>> > I also tried to divide the norm by m*n , which is the number of
>>>>>>>>> grids, the trend of norm still increases.
>>>>>>>>> >
>>>>>>>>> > Thanks!
>>>>>>>>> >
>>>>>>>>> > Weizhuo
>>>>>>>>> >
>>>>>>>>> > Matthew Knepley <knepley at gmail.com>
>>>>>>>>> > On Mon, Oct 1, 2018 at 6:31 PM Weizhuo Wang <
>>>>>>>>> weizhuo2 at illinois.edu> wrote:
>>>>>>>>> > Hi!
>>>>>>>>> >
>>>>>>>>> > I'm recently trying out the example code provided with the KSP
>>>>>>>>> solver (ex12.c). I noticed that the mean norm of the grid increases as I
>>>>>>>>> use finer meshes. For example, the mean norm is 5.72e-8 at m=10 n=10.
>>>>>>>>> However at m=100, n=100, mean norm increases to 9.55e-6. This seems counter
>>>>>>>>> intuitive, since most of the time error should decreases when using finer
>>>>>>>>> grid. Am I doing this wrong?
>>>>>>>>> >
>>>>>>>>> > The norm is misleading in that it is the l_2 norm, meaning just
>>>>>>>>> the sqrt of the sum of the squares of
>>>>>>>>> > the vector entries. It should be scaled by the volume element to
>>>>>>>>> approximate a scale-independent
>>>>>>>>> > norm (like the L_2 norm).
>>>>>>>>> >
>>>>>>>>> >   Thanks,
>>>>>>>>> >
>>>>>>>>> >      Matt
>>>>>>>>> >
>>>>>>>>> > Thanks!
>>>>>>>>> > --
>>>>>>>>> > Wang Weizhuo
>>>>>>>>> >
>>>>>>>>> >
>>>>>>>>> > --
>>>>>>>>> > 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/
>>>>>>>>> <https://urldefense.proofpoint.com/v2/url?u=https-3A__www.cse.buffalo.edu_-7Eknepley_&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=hsLktHsuxNfF6zyuWGCN8x-6ghPYxhx4cV62Hya47oo&m=KjmDEsZ6w8LEry7nlv3Bw7-pczqWbKGueFU59VoIWZg&s=tEv9-AHhL2CIlmmVos0gFa5PAY9oMG3aTQlnfi62ivA&e=>
>>>>>>>>> >
>>>>>>>>> >
>>>>>>>>> > --
>>>>>>>>> > Wang Weizhuo
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> --
>>>>>>>> Wang Weizhuo
>>>>>>>>
>>>>>>>
>>>>>>
>>>>>> --
>>>>>> Wang Weizhuo
>>>>>>
>>>>>
>>>>
>>>> --
>>>> Wang Weizhuo
>>>>
>>>
>>>
>>> --
>>> 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/>
>>>
>>
>>
>> --
>> Wang Weizhuo
>>
>
>
> --
> 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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