[petsc-users] projection methods in TS

[Matthew Knepley]

On Sat, Feb 4, 2017 at 7:56 PM, Zhang, Hong <hongzhang at anl.gov> wrote:

> On Feb 4, 2017, at 7:47 PM, Matthew Knepley <knepley at gmail.com> wrote:
>
> On Sat, Feb 4, 2017 at 7:44 PM, Jed Brown <jed at jedbrown.org> wrote:
>
>> Matthew Knepley <knepley at gmail.com> writes:
>>
>> > On Sat, Feb 4, 2017 at 7:24 PM, Zhang, Hong <hongzhang at anl.gov> wrote:
>> >
>> >> Can you elaborate a bit more on your problem?
>> >>
>> >> If your problem is an index-1 DAE, there is no need to use a projection
>> >> method, and it is perfectly fine to set it up as a DAE in PETSc. For
>> >> high-index DAEs, you may have to use TSSetPostStep() to implement your
>> own
>> >> projection algorithm.
>> >>
>> >
>> > Please define index.
>>
>> Think of it as a measure of singularity of the "mass matrix".  Higher
>> index DAE have more complicated constraints on compatibility of initial
>> conditions.  It's covered in any book or paper on DAEs.
>>
>
> Both your explanation and Hong's use of the term do not help Gideon (or
> me) know whether he has an index-1 DAE. There has
> to be some simple form you can write down so that we can tell.
>
>
> This is why we need to learn more about Gideon's problem. It is easy to
> determine the index if he can write down his problem in a simple form. But
> it is not that easy the other way round.
>

He says

  y' = f(y)

  0  = g(y)

which appears to me to be a Hessenberg index-2 DAE. Is that correct?

   Matt

Hong
>
>
>    Matt
>
> --
> 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
>
>
>


-- 
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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