[petsc-users] GAMG

[Jed Brown]

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.
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