[petsc-users] Increasing norm with finer mesh

[Weizhuo Wang]

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?

[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
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