ksp ex29.c B.C.s and Forcing terms.

[Matthew Knepley]

On Sat, Dec 12, 2009 at 4:34 PM, Ryan Yan <vyan2000 at gmail.com> wrote:

> Hi Barry,
> Since the ex32.c has been brought up to make comparison with ex29.c. Can I
> just get a confirm that, in ex29.c, the instance with Neumann B.C.s is the
> case where one has cell centered unknown for the u, with vertex centered f.
>

No, Neumann constraints mean that we fix the normal derivative of the
potential rather than the potential itself on the boundary.

  Matt


> Feel free to criticize this comment please, and this is where I get very
> confused.
>
> Thanks,
>
> Yan
>
>
>
> On Sat, Dec 12, 2009 at 2:57 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>
>>
>> On Dec 12, 2009, at 12:31 PM, Tahar Amari wrote:
>>
>>  Hello,
>>>
>>> SOrry. I took this very interesting discussion a bit late, but one of my
>>> major problem is to understand if all this is valid for node centered
>>> variables for u or cell centered.
>>> Usually the best way of solving Neuwman BC for this equation is having
>>> cell centered unknowns to have derivatives
>>> given on the domain boundary.
>>> This then have some impact on handling ghost values transfer between
>>> subdomains with MPI.Is all this transparent for
>>> us and PETSC handle it . I guess no, right ?
>>>
>>
>>  If you have only cell centered unknowns the ghost point updates are the
>> same. See src/ksp/ksp/examples/tutorials/ex32.c  Having some Neuman and some
>> Dirichlet boundary conditions is then trickery with cell centered.
>>
>>   If you have some cell-centered and some vertex centered unknowns
>> (staggered grid), DA does not handle this well, you have to "cheat" to match
>> up variables on the cells and vertices.
>>
>>
>>   Barry
>>
>>
>>
>>> Tahar
>>>
>>>
>>> Le 12 déc. 09 à 02:28, Barry Smith a écrit :
>>>
>>>
>>>> On Dec 11, 2009, at 7:18 PM, Ryan Yan wrote:
>>>>
>>>>  Hi Matt,
>>>>> Thank you very much for the reply.  Now, I got the Neumann part. But I
>>>>> am still a bit confused about the Dirichlet part. Please see the following
>>>>> quote.
>>>>>
>>>>> Yan
>>>>>
>>>>>
>>>>> For the Dirichlet B.C.s, I did not understand the coefficients given
>>>>> below. Isn't correct to set the v[0]=Hx*Hy here?
>>>>> if (i==0 || j==0 || i==mx-1 || j==my-1) {
>>>>> if (user->bcType == DIRICHLET) {
>>>>> v[0] = 2.0*rho*(HxdHy + HydHx);
>>>>> }
>>>>> }
>>>>>
>>>>> This is the proper scaling.
>>>>>
>>>>> the Dirichlet B.C.s:
>>>>> Which  scaling  do you think is proper, "v[0]=Hx*Hy" or 2.0*rho*(HxdHy
>>>>> + HydHx)?
>>>>> If it is 2.0*rho*(HxdHy + HydHx), can you say a little bit more about
>>>>> why is this one? I only see a factor of Hx*Hy when we set up the  RHS. Did I
>>>>> miss something?
>>>>>
>>>>>   Ryan,
>>>>
>>>>   You can scale the equations for Dirichlet boundary conditions anyway
>>>> you want; you could multiply them by 1,000,000 if you want. The answer in
>>>> exact precision with direct solvers will be the same. The reason we use the
>>>> given scaling is to make the scaling work well with multigrid. If you use a
>>>> different scaling the Dirichlet boundary conditions on the coarser grid
>>>> matrices would have a different scaling then the interior equations and this
>>>> would slow down MG's convergence rate. For toy problems people usually
>>>> eliminate the Dirichlet boundary conditions, then there is no scaling issue
>>>> for multigrid.
>>>>
>>>>
>>>>  Barry
>>>>
>>>>
>>>>> Matt
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> --
>>>>> 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
>>>>>
>>>>>
>>> --------------------------------------------
>>> T. Amari
>>> Centre de Physique Theorique
>>> Ecole Polytechnique
>>> 91128 Palaiseau Cedex France
>>> tel : 33 1 69 33 42 52
>>> fax: 33 1 69 33 49 49
>>> email: <mailto:amari at cpht.polytechnique.fr>
>>> URL : http://www.cpht.polytechnique.fr/cpht/amari
>>>
>>>
>>>
>>>
>>>
>>>
>>
>


-- 
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
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