[petsc-users] Nullspace issue

[Barry Smith]

  Thomas,

    Since you are solving a coupled system of equations you should start with PCFIELDSPLIT. This allows you to build a preconditioner by combining solvers for separate components of the PDE. It can even be applied recursively to first separate the Navier-Stokes equations from the Cahn-Hillard and then to separate the parts of the Navier-Stokes. 

    It may take a little thought for how you want the separation done and what solvers to use on what parts, but it is the only way to get an efficient solver for such a coupled system.

   Barry

  Jed, WTF are you talking about SVDs and stuff?


On Jun 12, 2012, at 8:19 AM, Thomas Witkowski wrote:

> Am 12.06.2012 15:04, schrieb Jed Brown:
>> On Tue, Jun 12, 2012 at 7:56 AM, Thomas Witkowski <thomas.witkowski at tu-dresden.de> wrote:
>> There should be no null space from the Cahn-Hilliard equation.
>> 
>> You said all those boundary conditions are either Neumann or periodic. I guess it couples to the fluid variables without any null space?
> yes.
>>  
>> Is there some black-box preconditioner that does not relay on LU factorization at some point? I know that black-box approaches are mostly not efficient, but I would have something I can work with.
>> 
>> The SVD always works and will tell you about a null space, but of course it's very expensive.
> So assume I have a basis for the null space of the system that should be solved. Is there any block-box solver/preconditioner approach that does not make use of (I)LU factorization at any point?
> 
> Thomas
>