[petsc-users] gamg student questions

[Matthew Knepley]

On Sun, Oct 17, 2021 at 9:04 AM Mark Adams <mfadams at lbl.gov> wrote:

> Hi Daniel, [this is a PETSc users list question so let me move it there]
>
> The behavior that you are seeing is a bit odd but not surprising.
>
> First, you should start with simple problems and get AMG (you might want
> to try this exercise with hypre as well: --download-hypre and use -pc_type
> hypre, or BDDC, see below).
>

We have two examples that do this:

  1) SNES ex56: This shows good performance of GAMG on Q1 and Q2 elasticity

  2) SNES ex17: This sets up a lot of finite element elasticity problems
where you can experiment with GAMG, ML, Hypre, BDDC, and other
preconditioners

As a rule of thumb, if my solver is taking more than 100 iterations
(usually for 1e-8 tolerance), something is very wrong. Either the problem
is setup incorrectly, the solver is
configured incorrectly, or I need to switch solvers.

  Thanks,

     Matt


> There are, alas, a lot of tuning parameters in AMG/DD and I recommend a
> homotopy process: you can start with issues that deal with your
> discretization on a simple cube, linear elasticity, cube elements, modest
> Posson ratio, etc., and first get "textbook multigrid efficiency" (TME),
> which for elasticity and a V(2,2) cycle in GAMG is about one digit of error
> reduction per iteration and perfectly monotonic until it hits floating
> point precision.
>
> I would set this problem up and I would hope it runs OK, but the
> problems that you want to do are probably pretty hard (high order FE,
> plasticity, incompressibility) so there will be more work to do.
>
> That said, PETSc has nice domain decomposition solvers that are more
> optimized and maintained for elasticity. Now that I think about it, you
> should probably look at these (
> https://petsc.org/release/docs/manualpages/PC/PCBDDC.html
> https://petsc.org/release/docs/manual/ksp/#balancing-domain-decomposition-by-constraints).
> I think they prefer, but do not require, that you do not assemble your
> element matrices, but let them do it. The docs will make that clear.
>
> BSSC is great but it is not magic, and it is no less complex, so I would
> still recommend the same process of getting TME and then moving to the
> problems that you want to solve.
>
> Good luck,
> Mark
>
>
>
> On Sat, Oct 16, 2021 at 10:50 PM Daniel N Pickard <pickard at mit.edu> wrote:
>
>> Hi Dr Adams,
>>
>>
>> I am using the gamg in petsc to solve some elasticity problems for
>> modeling bones. I am new to profiling with petsc, but I am observing that
>> around a thousand iterations my norm has gone down 3 orders of magnitude
>> but the solver slows down and progress sort of stalls. The norm
>> also doesn't decrease monotonically, but jumps around a bit. I also notice
>> that if I request to only use 1 multigrid level, the preconditioner is
>> much cheaper and not as powerful so the code takes more iterations, but
>> runs 2-3x faster. Is this expected that large models require lots of
>> iterations and convergence slows down as we get more accurate? What exactly
>> should I be looking for when I am profiling to try to understand how to run
>> faster? I see that a lot of my ratio's are 2.7, but I think that is because
>> my mesh partitioner is not doing a great job making equal domains. What are
>> the giveaways in the log_view that tell you that petsc could be optimized
>> more?
>>
>>
>> Also when I look at the solution with just 4 orders of magnitude of
>> convergence I can see that the solver has not made much progress in the
>> interior of the domain, but seems to have smoothed out the boundary where
>> forces where applied very well. Does this mean I should use a larger
>> threshold to get more course grids that can fix the low frequency error?
>>
>>
>> Thanks,
>>
>> Daniel Pickard
>>
>

-- 
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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