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

[Brian Merchant]

Hi Barry,

Here's some non-trivial example code:
https://gist.github.com/bmer/2af429f88b0b696648a8

I have still made some simplifications by removing some phase variables,
expanding on variable names in general, and so on.

The rhs function itself is defined on line 578. The functions referred to
within it should be all defined above, so you can have a peek at them as
necessary.

Starting from line 634 I show how I use the rhs function. In particular,
note the "disjointed" evaluation of the integral -- I don't just evaluate
from 0 to t all at one go, but rather evaluate the integral in pieces
(let's call the time spent between the end of one integral evaluation, and
the start of the next integral evaluation a "pause"). This is so that if
there were multiple amoebas, during the "pause", I can take into account
changes in some of the parameters due to contact between one amoeba and
another -- poor man's simplification.

Please let me know if this is what you were looking for. I wouldn't be
surprised if it wasn't, but instead would be happy to try to rework what
I've got so it's more in line with what would be meaningful to you.

Kind regards,
Brian

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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