[petsc-users] Help for MatNullSpaceCreateRigidBody

[Matthew Knepley]

On Mon, Dec 4, 2023 at 12:01 PM Jordi Manyer Fuertes via petsc-users <
petsc-users at mcs.anl.gov> wrote:

> Dear PETSc users/developpers,
>
> I am currently trying to use the method `MatNullSpaceCreateRigidBody`
> together with `PCGAMG` to efficiently precondition an elasticity solver
> in 2D/3D.
>
> I have managed to make it work in serial (or with 1 MPI rank) with
> h-independent number of iterations (which is great), but the solver
> diverges in parallel.
>
> I assume it has to do with the coordinate vector I am building the
> null-space with not being correctly setup. The documentation is not that
> clear on which nodes exactly have to be set in each partition. Does it
> require nodes corresponding to owned dofs, or all dofs in each partition
> (owned+ghost)? What ghost layout should the `Vec` have?
>
> Any other tips about what I might be doing wrong?
>

What we assume is that you have some elastic problem formulated in primal
unknowns (displacements) so that the solution vector looks like this:

  [ d^0_x d^0_y d^0_z d^1_x ..... ]

or whatever spatial dimension you have. We expect to get a global vector
that looks like that, but instead
of displacements, we get the coordinates that each displacement corresponds
to. We make the generators of translations:

  [ 1 0 0 1 0 0 1 0 0 1 0 0... ]
  [ 0 1 0 0 1 0 0 1 0 0 1 0... ]
  [ 0 0 1 0 0 1 0 0 1 0 0 1... ]

for which we do not need the coordinates, and then the generators of
rotations about each axis, for which
we _do_ need the coordinates, since we need to know how much each point
moves if you rotate about some center.

  Does that make sense?

   Thanks,

      Matt



> Thanks,
>
> Jordi
>
>

-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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