[petsc-users] Hessenberg Index-2 DAE and IMEX

[Matthew Knepley]

On Tue, Feb 15, 2022 at 1:39 PM Zhang, Hong via petsc-users <
petsc-users at mcs.anl.gov> wrote:

> Yes. I am talking about a general usage. To be accurate, direct
> application of these methods does not always work. There are examples of
> high-index DAEs for which backward Euler and all multi-step and RK methods
> fail. You can find one such example in
> https://www.cs.usask.ca/~spiteri/M314/notes/AP/chap10.pdf
> This note also mentions the difficulties in solving the nonlinear system
> and calculating error estimate for index-2 DAEs.
>
> Thus we do not recommend solving index-2 DAEs directly with these methods.
>

I have an index-2 DAE (earthquake mechanics), and we had to explicitly
differentiate the constraint and add terms back in the
momentum equation. This is also what is done for Navier-Stokes (I think
they call it a segregated timestepping method).

  Thanks,

     Matt


> Hong
>
> On Feb 15, 2022, at 10:27 AM, Tang, Qi <tangqi at msu.edu> wrote:
>
> Thanks a lot, Hong.
>
> I would think if one use BDF or backward Euler for incompressible Naiver
> Stokes, it should work with the index 2 equation. Why do you think it will
> not work? Or maybe you were talking about a general usage.
>
> INS is not my usage but I am still curious. We have some unconventional
> constraint equation.
>
> Qi
>
>
>
> On Feb 15, 2022, at 8:51 AM, Zhang, Hong <hongzhang at anl.gov> wrote:
>
> Hi Qi,
>
> The index-2 DAE cannot be solved directly with ARK or implicit methods
> such as backward Euler and Crank-Nicolson. You need to convert the system
> to an index-1 DAE as illustrated in the documentation.
>
> Hong (Mr.)
>
> On Feb 15, 2022, at 9:43 AM, Tang, Qi <tangqi at msu.edu> wrote:
>
> Hi,
>
> Does PETSc’s ARK directly apply to Hessenberg Index-2 DAE? Do we need to
> perform a time derivative of the constraint equation by ourselves first?
> https://petsc.org/main/docs/manual/ts/#hessenberg-index-2-dae
> <https://urldefense.com/v3/__https://petsc.org/main/docs/manual/ts/*hessenberg-index-2-dae__;Iw!!HXCxUKc!kM_qeX09WwLuE991Vn6u85M0vDlNnqMA0Diuy84sqZawkGLr-MNDkYVisStQBA$>
> If we do not have to, do we expect to get high order in time?
>
> Thanks,
> Qi
>
>
>
>
>
>
>

-- 
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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