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

[Barry Smith]

   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
>