[petsc-users] Is it still worth switching to PETSc if I can't write a Jacobian for my problem?

[Brian Merchant]

Alright, I can get that for you! Thank you very much for your time!

On Wed, Dec 9, 2015 at 2:18 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:

>
>   I prefer the actual code, not the mathematics or the explanation
>
> > On Dec 9, 2015, at 3:42 PM, Brian Merchant <bhmerchant at gmail.com> wrote:
> >
> > Hi Barry,
> >
> > > Could send an example of your "rhs" function; not a totally trivial
> example
> >
> > Sure thing! Although, did you check out the exam I tried to build up in
> this stackexchange question, along with a picture:
> http://scicomp.stackexchange.com/questions/21501/is-it-worth-switching-to-timesteppers-provided-by-petsc-if-i-cant-write-down-a
> >
> > I ask because that's probably the best I can do without using as little
> math as possible.
> >
> > Otherwise, what I'll do is take a couple of days to carefully look at my
> work, and write up a non-trivial example of a difficult-to-differentiate
> RHS, that still is a simplification of the whole mess -- expect a one or
> two page PDF?
> >
> > Kind regards,
> > Brian
> >
> > On Mon, Dec 7, 2015 at 12:45 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
> >
> >    Brian,
> >
> >     Could send an example of your "rhs" function; not a totally trivial
> example
> >
> >    Barry
> >
> > > On Dec 7, 2015, at 11:21 AM, Brian Merchant <bhmerchant at gmail.com>
> wrote:
> > >
> > > Hi all,
> > >
> > > I am considering using petsc4py instead of scipy.integrate.odeint
> (which is a wrapper for Fortran solvers) for a problem involving the
> solution of a system of ODEs. The problem has the potential to be stiff.
> Writing down its Jacobian is very hard.
> > >
> > > So far, I have been able to produce reasonable speed gains by writing
> the RHS functions in "something like C" (using either numba or Cython). I'd
> like to get even more performance out, hence my consideration of PETSc.
> > >
> > > Due to the large number of equations involved, it is already tedious
> to think about writing down a Jacobian. Even worse though, is that some of
> the functions governing a particular interaction do not have neat
> analytical forms (let alone whether or not their derivatives have neat
> analytical forms), so we might have a mess of piecewise functions needed to
> approximate them if we were to go about still trying to produce a
> Jacobian...
> > >
> > > All the toy examples I see of PETSc time stepping problems have
> Jacobians defined, so I wonder if I would even get a speed gain going from
> switching to it, if perhaps one of the reasons why I have a high
> computational cost is due to not being able to provide a Jacobian function?
> > >
> > > I described the sort of problem I am working with in more detail in
> this scicomp.stackexchange question, which is where most of this question
> is copied from, except it also comes with a toy version of the problem I am
> dealing with:
> http://scicomp.stackexchange.com/questions/21501/is-it-worth-switching-to-timesteppers-provided-by-petsc-if-i-cant-write-down-a
> > >
> > > All your advice would be most helpful :)
> > >
> > > Kind regards,Brian
> > >
> >
> >
>
>
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