[petsc-users] GAMG

[Kong, Fande]

On Mon, Oct 31, 2016 at 8:44 AM, Jed Brown <jed at jedbrown.org> wrote:

> Jeremy Theler <jeremy at seamplex.com> writes:
>
> > Hi again
> >
> > I have been wokring on these issues. Long story short: it is about the
> > ordering of the unknown fields in the vector.
> >
> > Long story:
> > The physics is linear elastic problem, you can see it does work with LU
> > over a simple cube (warp the displacements to see it does represent an
> > elastic problem, E=200e3, nu=0.3):
> >
> > https://caeplex.com/demo/results.php?id=5817146bdb561
> >
> >
> > Say my three displacements (unknowns) are u,v,w. I can define the
> > unknown vector as (is this called node-based ordering?)
> >
> > [u1 v1 w1 u2 v2 w2 ... un vn wn]^T
> >
> > Another option is (is this called unknown-based ordering?)
> >
> > [u1 u2 ... un v1 v2 ... vn w1 w2 ... wn]^T
> >
> >
> > With lu/preonly the results are the same, although the stiffnes matrixes
> > for each case are attached as PNGs. And of course, the near-nullspace
> > vectors are different. So PCSetCoordinates() should work with one
> > ordering and not with another one, an issue I did not take into
> > consideration.
> >
> > After understanding Matt's point about the near nullspace (and reading
> > some interesting comments from Jed on scicomp stackexchange) I did built
> > my own vectors (I had to take a look at MatNullSpaceCreateRigidBody()
> > because I found out by running the code the nullspace should be an
> > orthonormal basis, it should say so in the docs).
>
> Where?
>
> "vecs   - the vectors that span the null space (excluding the constant
> vector); these vectors must be orthonormal."
>
> https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/
> MatNullSpaceCreate.html
>
> And if you run in debug mode (default), as you always should until you
> are confident that your code is correct, MatNullSpaceCreate tests that
> your vectors are orthonormal.
>
> > Now, there are some results I do not understand. I tried these six
> > combinations:
> >
> > order      near-nullspace       iterations    norm
> > -----      --------------       ----------    ----
> > unknown    explicit             10            1.6e-6
> > unknown    PCSetCoordinates     15            1.7e-7
> > unknown    none                 15            2.4e-7
> > node       explicit             fails with error -11
> > node       PCSetCoordinates     fails with error -11
> > node       none                 13            3.8e-7
>
> Did you set a block size for the "node-based" orderings?  Are you sure
> the above is labeled correctly?  Anyway, PCSetCoordinates uses
> "node-based" ordering.  Implementation performance will generally be
> better with node-based ordering -- it has better memory streaming and
> cache behavior.
>
> The AIJ matrix format will also automatically do an "inode" optimization
> to reduce memory bandwidth and enable block smoothing (default
> configuration uses SOR smoothing).  You can use -mat_no_inode to try
> turning that off.
>
> > Error -11 is
> > PETSc's linear solver did not converge with reason
> > 'DIVERGED_PCSETUP_FAILED' (-11)
>
> Isn't there an actual error message?
>
> > Any explanation (for dumbs)?
> > Another thing to take into account: I am setting the dirichlet BCs with
> > MatZeroRows(), but I am not updating the columns to keep symmetry. Can
> > this pose a problem for GAMG?
>
> Usually minor, but it is better to maintain symmetry.
>

If the boundary values are not zero, no way to maintain symmetry unless we
reduce the extra part of  the matrix. Not updating the columns is better in
this situation.

Fande,
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