[petsc-users] VI: RS vs SS

[Alexander Lindsay]

On Thu, Oct 24, 2019 at 4:52 AM Munson, Todd <tmunson at mcs.anl.gov> wrote:

>
> Hi,
>
> For these problems, how large are they?  And are they linear or
> nonlinear?
> What I can do is use some fancier tools to help with what is going on with
> the solvers in certain cases.
>

For the results cited above:

100 elements -> 101 dofs
1,000 elements -> 1,001 dofs
10,000 elements -> 10,001 dofs

The PDE is linear with simple bounds constraints on the variable: 0 <= u <=
10


> For Barry's question, the matrix in the SS solver is a diagonal matrix plus
> a column scaling of the Jacobian.
>
> Note: semismooth, reduced space and interior point methods mainly work for
> problems that are strictly monotone.


Dumb question, but monotone in what way?

Thanks for the replies!

Alex

Finding out what is going on with
> your problems with some additional diagnostics might yield some
> insights.
>
> Todd.
>
> > On Oct 24, 2019, at 3:36 AM, Smith, Barry F. <bsmith at mcs.anl.gov> wrote:
> >
> >
> > See bottom
> >
> >
> >> On Oct 14, 2019, at 1:12 PM, Justin Chang via petsc-users <
> petsc-users at mcs.anl.gov> wrote:
> >>
> >> It might depend on your application, but for my stuff on maximum
> principles for advection-diffusion, I found RS to be much better than SS.
> Here’s the paper I wrote documenting the performance numbers I came across
> >>
> >> https://www.sciencedirect.com/science/article/pii/S0045782516316176
> >>
> >> Or the arXiV version:
> >>
> >> https://arxiv.org/pdf/1611.08758.pdf
> >>
> >>
> >> On Mon, Oct 14, 2019 at 1:07 PM Alexander Lindsay via petsc-users <
> petsc-users at mcs.anl.gov> wrote:
> >> I've been working on mechanical contact in MOOSE for a while, and it's
> led to me to think about general inequality constraint enforcement. I've
> been playing around with both `vinewtonssls` and `vinewtonrsls`. In
> Benson's and Munson's Flexible Complementarity Solvers paper, they were
> able to solve 73.7% of their problems with SS and 65.5% with RS which led
> them to conclude that the SS method is generally more robust.  We have had
> at least one instance where a MOOSE user reported an order of magnitude
> reduction in non-linear iterations when switching from SS to RS. Moreover,
> when running the problem described in this issue, I get these results:
> >>
> >> num_elements = 100
> >> SS nl iterations = 53
> >> RS nl iterations = 22
> >>
> >> num_elements = 1000
> >> SS nl iterations = 123
> >> RS nl iterations = 140
> >>
> >> num_elements = 10000
> >> SS: fails to converge within 50 nl iterations during the second time
> step whether using a `basic` or `bt` line search
> >> RS: fails to converge within 50 nl iterations during the second time
> step whether using a `basic` or `bt` line search (although I believe
> `vinewtonrsls` performs a line-search that is guaranteed to keep the
> degrees of freedom within their bounds)
> >>
> >> So depending on the number of elements, it appears that either SS or RS
> may be more performant. I guess since I can get different relative
> performance with even the same PDE, it would be silly for me to ask for
> guidance on when to use which? In the conclusion of Benson's and Munson's
> paper, they mention using mesh sequencing for generating initial guesses on
> finer meshes. Does anyone know whether there have been any publications
> using PETSc/TAO and mesh sequencing for solving large VI problems?
> >>
> >> A related question: what needs to be done to allow SS to run with
> `-snes_mf_operator`? RS already appears to support the option.
> >
> >   This may not make sense. Is the operator used in the SS solution
> process derivable from the function that is being optimized with the
> constraints or some strange scaled beast?
> >>
> >
>
>
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