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

Matthew Knepley knepley at gmail.com
Fri Aug 17 14:39:42 CDT 2012

```On Fri, Aug 17, 2012 at 2:27 PM, Thomas Witkowski <
thomas.witkowski at tu-dresden.de> wrote:

>  On Fri, Aug 17, 2012 at 3:10 AM, Thomas Witkowski <
> 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.
>

What is your evidence that it has a null space?

Matt

>
> Thomas
>

--
What most experimenters take for granted before they begin their
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