[petsc-users] SNES and TS for nonlinear quasi-static problems

[Jed Brown]

Indeed, this is exactly how we do quasistatic analysis for solid mechanics in Ratel (https://gitlab.com/micromorph/ratel) -- make sure to choose an L-stable integrator (backward Euler being the most natural choice). Implicit dynamics can be done by choosing a suitable integrator, like TSALPHA2, with almost no code change to the residual (only adding the mass term in DMTSSetI2Function()).

Matthew Knepley <knepley at gmail.com> writes:

> On Mon, Dec 19, 2022 at 6:12 AM TARDIEU Nicolas via petsc-users <
> petsc-users at mcs.anl.gov> wrote:
>
>> Dear PETSc users,
>>
>> I plan to solve nonlinear quasi-static problems with PETSc. More
>> precisely, these are solid mechanics problems with elasto-plasticity.
>> So they do not involve  "physical time", rather  "pseudo time", which is
>> mandatory to describe the stepping of the loading application.
>> In general, the loading vector F(x, t) is expressed as the following
>> product  F(x, t)=F0(x)*g(t), where g is a scalar function of the
>> pseudo-time.
>>
>> I see how to use a SNES in order to solve a certain step of the loading
>> history but I wonder if a TS can be used to deal with the loading history
>> through the definition of this g(t) function ?
>>
>
> I believe so. We would want you to formulate it as a differential equation,
>
>   F(x, \dot x, t) = G(x)
>
> which is your case is easy
>
>   F(x, t) = 0
>
> so you would just put your function completely into the IFunction. Since
> there is no \dot x term, this is a DAE,
> and you need to use one of the solvers for that.
>
>
>> Furthermore, since too large load steps can lead to non-convergence, a
>> stepping strategy is almost always required to restart a load step that
>> failed. Does TS offer such a feature ?
>>
>
> I think you can use PETSc adaptation. There is a PID option, which might be
> able to capture your behavior.
>
>   Thanks,
>
>       Matt
>
>
>> Thank you for your answers.
>> Regards,
>> Nicolas
>> --
>> *Nicolas Tardieu*
>> *Ing PhD Computational Mechanics*
>> EDF - R&D Dpt ERMES
>> PARIS-SACLAY, FRANCE
>>
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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
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> -- Norbert Wiener
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> https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>