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

[Zhang, Hong]

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.

Hong

On Feb 15, 2022, at 10:27 AM, Tang, Qi <tangqi at msu.edu<mailto: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<mailto: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<mailto: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






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