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

[Tahar Amari]

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 ?

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
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