[petsc-users] Increasing norm with finer mesh

[Matthew Knepley]

On Mon, Oct 1, 2018 at 8:51 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.
>

We need to be precise. First, look at the initial residual, because that is
what you control with the initial
guess. You are saying that the initial residual does not asymptote? I would
be reluctant to believe that.

  Thanks,

     Matt


> Thanks!
>
> Weizhuo
>
> Matthew Knepley <knepley at gmail.com> 于2018年10月1日周一 下午7:45写道：
>
>> 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/
>> <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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