[petsc-users] Nullspace for a coupled system of equations

[Thomas Witkowski]

On Fri, Aug 17, 2012 at 3:10 AM, Thomas Witkowski 
<thomas.witkowski at tu-dresden.de <mailto:thomas.witkowski at tu-dresden.de>> 
wrote:
>
>>         I want to solve some (weakly) coupled system of equations of
>>         the following form:
>>
>>         A  B     u
>>                 .     =   .....
>>         0  C     v
>>
>>
>>         so, C is the discrete Laplacian and A and B are some more
>>         complicated operators (I make use of linear finite elements).
>>         All boundary conditions are periodic, so the unknown v is
>>         determined only up to a constant. A and B contain both the
>>         identity operator, so u is fixed. Now I want to solve the
>>         system on the whole (there are reasons to do it in this way!)
>>         and I must provide information about the nullspace to the
>>         solver. When I am right, to provide the correct nullspace I
>>         must solve one equation with A. Is there any way in PETSc to
>>         circumvent the problem?
>>
>>
>>     If I understand you correctly, your null space vector is (0 I). I
>>     use the same null space for SNES ex62.
>     (0 I) cannot be an element of the null space, as multiplying it
>     with the matrix results in a non-zero vector. Or am I totally
>     wrong about null spaces of matrices?
>
>
> Maybe you could as your question again. I am not understanding what 
> you want.
>
I want to solve the block triangular system as described above. My 
problem is, that it has a one dimensional null space, but I'm not able 
to define it. My question is: does anyone can give me an advice how to 
EITHER compute the null space explicitly OR how to solve the system in 
such a way that the null space is considered by the solver. The only 
constraint is that I cannot split the system of equations into two 
independent solve for both variables. I know that from this description 
its not clear why there is this constraint, but it would take too long 
to describe it.

Thomas
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