[petsc-users] GAMG

[Matthew Knepley]

On Mon, Oct 31, 2016 at 10:29 AM, Kong, Fande <fande.kong at inl.gov> wrote:

> 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.
>

?

You just eliminate the unknowns.

   Matt


>
> Fande,
>
>
>
>


-- 
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
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