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

[Thomas Witkowski]

Am 17.08.2012 16:24, schrieb Matthew Knepley:
> 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?

Thomas

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