[petsc-users] Effect of -pc_gamg_threshold vs PETSc version

[Mark Adams]

OK, P2 tets linear elasticity. That is good to know.

Matt, there were a bunch of changes, mostly "small", but a big change was
(2.18) changing the aggressive coarsening (square graph) from MIS(A'A) to
MIS(MIS(A)).
In my experiments, the coarsening rates changed a little.
2.17 went from SOR to Jacobi default smoothing, and Jeremy's times went
down a little. idk.

Jeremy, you may want more levels of aggressive coarsening with P2 tests.
The old syntax will work but the new is -pc_gamg_aggressive_coarsening <1>

More to come,
Mark


On Fri, Apr 14, 2023 at 9:56 AM Matthew Knepley <knepley at gmail.com> wrote:

> On Fri, Apr 14, 2023 at 8:54 AM Jeremy Theler <jeremy at seamplex.com> wrote:
>
>> Hi Mark. So glad you answered.
>>
>> > 0) what is your test problem? eg, 3D Lapacian with Q1 finite
>> > elements.
>>
>> I said in my first email it was linear elasticty (and I gave a link
>> where you can see the geometry, BCs, etc.) but I did not specifty
>> further details.
>> It is linear elasticity with displacement-based FEM formulation using
>> unstructured curved 10-noded tetrahedra.
>>
>
> I believe our jargon for this would be "P_2 Lagrange element".
>
>
>> The matrix is marked as SPD with MatSetOption() and the solver is
>> indeed CG and not the default GMRES.
>>
>> > First, you can get GAMG diagnostics by running with '-info :pc' and
>> > grep on GAMG.
>>
>> Great advice. Now I have a lot more of information but I'm not sure how
>> to analyze it. Find attached for each combination of threshold and
>> PETSc version the output of -info :pc -ksp_monitor -ksp_view
>>
>> In general it looks like 3.18 and 3.19 have less KSP iterations than
>> 3.17 but the overall time is larger.
>>
>
> I will also look and see if I can figure out the change. This kind of
> behavior usually means that
> we somehow made the coarse problem larger. This can make it more accurate
> (fewer iterations)
> but more costly. This also makes sense that it is sensitive to the
> threshold parameter, but that is
> not the only thing that controls the sparsity. There is also squaring the
> graph.
>
> Mark, do you know if we change the default for squaring?
>
>   Thanks,
>
>     Matt
>
>
>> > Anyway, sorry for the changes.
>> > I hate changing GAMG for this reason and I hate AMG for this reason!
>>
>> No need to apologize, I just want to better understand how to better
>> exploit your code!
>>
>> Thanks
>> --
>> jeremy
>>
>> >
>> > Thanks,
>> > Mark
>> >
>> >
>> >
>> > On Thu, Apr 13, 2023 at 8:17 AM Jeremy Theler <jeremy at seamplex.com>
>> > wrote:
>> > > When using GAMG+cg for linear elasticity and providing the near
>> > > nullspace computed by MatNullSpaceCreateRigidBody(), I used to find
>> > > "experimentally" that a small value of -pc_gamg_threshold in the
>> > > order
>> > > of 0.0001 would slightly decrease the solve time.
>> > >
>> > > Starting with 3.18, I started seeing that any positive value for
>> > > the
>> > > treshold would increase the solve time. I did a quick parametric
>> > > (serial) run solving an elastic problem with a matrix size of
>> > > approx
>> > > 570k x 570k for different values of GAMG threshold and different
>> > > PETSc
>> > > versions (compiled with the same compiler, options and flags).
>> > >
>> > > I noted that
>> > >
>> > >  1. starting from 3.18, a threshold of 0.0001 that used to improve
>> > > the
>> > > speed now worsens it.
>> > >  2. PETSc 3.17 looks like a "sweet spot" of speed
>> > >
>> > > I would like to hear any comments you might have.
>> > >
>> > > The wall time shown includes the time needed to read the mesh and
>> > > assemble the stiffness matrix. It is a refined version of the
>> > > NAFEMS
>> > > LE10 benchmark described here:
>> > > https://seamplex.com/feenox/examples/mechanical.html#nafems-le10-
>> > > thick-plate-pressure-benchmark
>> > >
>> > > If you want, I could dump the matrix, rhs and near nullspace
>> > > vectors
>> > > and share them.
>> > >
>> > > --
>> > > jeremy theler
>> > >
>>
>>
>
> --
> 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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