[petsc-users] Increasing norm with finer mesh

[Mark Adams]

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> 于2018年10月2日周二 下午2:27写道：
>
>>
>>
>> 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
>
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