[petsc-users] Increasing norm with finer mesh

[Weizhuo Wang]

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:

[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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