[petsc-users] projection methods in TS

[Zhang, Hong]

On Feb 4, 2017, at 7:58 PM, Matthew Knepley <knepley at gmail.com<mailto:knepley at gmail.com>> wrote:

On Sat, Feb 4, 2017 at 7:56 PM, Zhang, Hong <hongzhang at anl.gov<mailto:hongzhang at anl.gov>> wrote:
On Feb 4, 2017, at 7:47 PM, Matthew Knepley <knepley at gmail.com<mailto:knepley at gmail.com>> wrote:

On Sat, Feb 4, 2017 at 7:44 PM, Jed Brown <jed at jedbrown.org<mailto:jed at jedbrown.org>> wrote:
Matthew Knepley <knepley at gmail.com<mailto:knepley at gmail.com>> writes:

> On Sat, Feb 4, 2017 at 7:24 PM, Zhang, Hong <hongzhang at anl.gov<mailto: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?

This is not a DAE form because neither f() nor g() contains the algebraic variable.

Hong


   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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