[petsc-users] Increasing norm with finer mesh

[Matthew Knepley]

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/>
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