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 <[email protected]> wrote:
> > 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 > > > > > > > > >
