[petsc-users] Increasing norm with finer mesh

[Matthew Knepley]

On Tue, Oct 16, 2018 at 9:14 PM Weizhuo Wang <weizhuo2 at illinois.edu> wrote:

> I just tried both, neither of them make a difference. I got exactly the
> same curve with either combination.
>

I have a hard time believing you. If you make the residual tolerance much
finer, your error will definitely change.
I run tests every day that do exactly this. You can run them too, since
they are just examples.

  Thanks,

     Matt


> Thanks!
>
> Wang weizhuo
>
> On Tue, Oct 16, 2018 at 8:06 PM Matthew Knepley <knepley at gmail.com> wrote:
>
>> On Tue, Oct 16, 2018 at 7:26 PM Weizhuo Wang <weizhuo2 at illinois.edu>
>> wrote:
>>
>>> Hello again!
>>>
>>> After some tweaking the code is giving right answers now. However it
>>> start to disagree with MATLAB results ('traditional' way using matrix
>>> inverse) when the grid is larger than 100*100. My PhD advisor and I
>>> suspects that the default dimension of the Krylov subspace is 100 in the
>>> test case we are running. If so, is there a way to increase the size of the
>>> subspace?
>>>
>>
>> 1) The default subspace size is 30, not 100. You can increase the
>> subspace size using
>>
>>        -ksp_gmres_restart n
>>
>> 2) The problem is likely your tolerance. The default solver tolerance is
>> 1e-5. You can change it using
>>
>>        -ksp_rtol 1e-9
>>
>>   Thanks,
>>
>>      Matt
>>
>>
>>>
>>> [image: Disagrees.png]
>>>
>>> Thanks!
>>>
>>> Wang Weizhuo
>>>
>>> On Tue, Oct 9, 2018 at 2:50 AM Mark Adams <mfadams at lbl.gov> wrote:
>>>
>>>> To reiterate what Matt is saying, you seem to have the exact solution
>>>> on a 10x10 grid. That makes no sense unless the solution can be represented
>>>> exactly by your FE space (eg, u(x,y) = x + y).
>>>>
>>>> On Mon, Oct 8, 2018 at 9:33 PM Matthew Knepley <knepley at gmail.com>
>>>> wrote:
>>>>
>>>>> On Mon, Oct 8, 2018 at 9:28 PM Weizhuo Wang <weizhuo2 at illinois.edu>
>>>>> wrote:
>>>>>
>>>>>> The code is attached in case anyone wants to take a look, I will try
>>>>>> the high frequency scenario later.
>>>>>>
>>>>>
>>>>> That is not the error. It is superconvergence at the vertices. The
>>>>> real solution is trigonometric, so your
>>>>> linear interpolants or whatever you use is not going to get the right
>>>>> value in between mesh points. You
>>>>> need to do a real integral over the whole interval to get the L_2
>>>>> error.
>>>>>
>>>>>   Thanks,
>>>>>
>>>>>      Matt
>>>>>
>>>>>
>>>>>> On Mon, Oct 8, 2018 at 7:58 PM Mark Adams <mfadams at lbl.gov> wrote:
>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> On Mon, Oct 8, 2018 at 6:58 PM Weizhuo Wang <weizhuo2 at illinois.edu>
>>>>>>> wrote:
>>>>>>>
>>>>>>>> The first plot is the norm with the flag -pc_type lu with respect
>>>>>>>> to number of grids in one axis (n), and the second plot is the norm without
>>>>>>>> the flag -pc_type lu.
>>>>>>>>
>>>>>>>
>>>>>>> So you are using the default PC w/o LU. The default is ILU. This
>>>>>>> will reduce high frequency effectively but is not effective on the low
>>>>>>> frequency error. Don't expect your algebraic error reduction to be at the
>>>>>>> same scale as the residual reduction (what KSP measures).
>>>>>>>
>>>>>>>
>>>>>>>>
>>>>>>
>>>>>> --
>>>>>> 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=http-3A__www.cse.buffalo.edu_-7Eknepley_&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=hsLktHsuxNfF6zyuWGCN8x-6ghPYxhx4cV62Hya47oo&m=EFM29ATgv4U8PjXEtfgMkuxKr5DGscMlH-j769W5W_4&s=grgSL2LaDCthvYvvFITmeOOWPCwgmNfYRPs94N8kmOs&e=>
>>>>>
>>>>
>>>
>>> --
>>> 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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