dolfin team mailing list archive

["Garth N. Wells" <gnw20@xxxxxxxxx>]

On Thu, Nov 1, 2012 at 7:52 AM, Anders Logg <logg@xxxxxxxxx> wrote:
> On Thu, Nov 01, 2012 at 07:49:03AM +0000, Garth N. Wells wrote:
>> I've added a demo for solving singular systems using a Krylov solver via PETSc:
>>
>>    demo/undocumented/singular
>>
>> This can provide a good alternative to, for example, pinning the
>> pressure in a Stokes problem or using a global Lagrange multiplier. In
>> contrast to pinning or Lagrange multipliers, it doesn't mess up
>> preconditioners or introduce a global row to the matrix.
>
> Very useful. What is exactly the logic of
>
> null_space = Vector(u.vector())
> V.dofmap().set(null_space, 1.0)
> solver.set_nullspace([null_space])
>
> ?
>
> Why does the dofmap need to be involved?
>

Because I don't otherwise know how to build the null space for
multi-field problems, e.g. elasticity which has six vectors in the
null space. The dofmap can set the entries in a vector that correspond
to a given field to a specified value. In the case of 3D Stokes,

    V.sub(3).dofmap().set(null_space, 1.0)

would build the null space for the pressure.

The demo is simple because the null space is spanned by just the
constant vector. I may add an option to
GenericLinearSolver::set_nullspace to add a constant without having to
build it explicitly.

Garth

>> Does anyone know if Trilinos/AztecOO has similar functionality to
>> PETSc for solving singular problems?
>
> No idea.
>
> --
> Anders