[petsc-users] [petsc-maint] Question about NewtonTR / Inexact Newton with piecewise continuous functions

[Matthew Knepley]

On Sun, Aug 24, 2025 at 8:16 PM Ali ALI AHMAD <ali.ali_ahmad at utt.fr> wrote:

> Hello,
>
> I am currently working with PETSc to solve a nonlinear system. My function
> is piecewise continuous (so it can be discontinuous), and its derivative
> (Jacobian) is also piecewise continuous.
>

I am not aware of any convergence framework for piecewise continuous
functions. They are not technically computable, meaning you could have to
compute for a very very long time, and still not get an accurate output
(since you have the jump). This also means that the derivative is not
computable, and you can have arbitrarily large errors near the
discontinuity. I don't see how you could prove convergence here, but maybe
someone else knows something I don't.

  Thanks,

      Matt


> I implemented the residual and also compute the Jacobian analytically.
>
> When the discontinuities are small, both Inexact Newton and NewtonTR (with
> scaled Newton direction) converge without problem.
>
> However, for test cases with larger discontinuities, sometimes the solver
> converges, but in other cases it fails to converge.
>
> I initially tried <vinewtonssls,vinewtonrsls> , but I cannot use them in
> my case, because my problem involves nonlinear constraints.
>
> So my question is: how does PETSc handle such situations internally
> (piecewise continuous objective/residual functions)?
> And is there a recommended strategy within PETSc to deal with nonlinear
> solvers when and are discontinuous?
>
> I would like to continue working with PETSc and I am looking for a robust
> method to treat this type of problem.
>
> Thank you very much for your help and suggestions.
>
> Best regards,
> ALI ALI AHMAD
>


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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

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