[petsc-users] VI: RS vs SS

[Justin Chang]

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
> <https://groups.google.com/d/msg/moose-users/Kzimz-HcK2s/y_jnCQGaCAAJ> in
> non-linear iterations when switching from SS to RS. Moreover, when running
> the problem described in this issue
> <https://gitlab.com/petsc/petsc/issues/411#note_229556542>, 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.
>
>
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