I prefer the actual code, not the mathematics or the explanation
> On Dec 9, 2015, at 3:42 PM, Brian Merchant <[email protected]> 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 <[email protected]> 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 <[email protected]> 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
> >
>
>
