[petsc-dev] nonlinear solvers

[Barry Smith]

On Jan 18, 2014, at 6:54 PM, Peter Brune <prbrune at gmail.com> wrote:

> From my initial reading of the paper, it's about a backtracking linesearch where you have a persistent-between-iterations parameter that increases or decreases, taking your damping less than or towards one based upon the difference between subsequent residual norms.

> 

    Thanks

     It is an example of a line search with persistent state that we do not currently have. Right?

>   I have no idea how it fits in as a post-check rather than as a line search, as it would be redundant.

   Agreed, it doesn’t belong as a post-check


>  It's not clear that this would be better than anything we have now.

    Agreed. But these are famous people so maybe there is some great subtly we are missing, or maybe not.

>  Are you sure that this is the right paper?

   Pretty sure. It is the in the link from the other paper.

   Barry

> 
> - Peter
> 
> On Sat, Jan 18, 2014 at 6:09 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
> 
>   Peter,
> 
>    What the hay is this R. E. Bank and D. J. Rose, ``Global Approximate Newton Methods,'' Numer. Math., vol. 37, pp. 279-295, 1981. and should it be a “line search” or something in SNES?
> 
>    Thanks
> 
>    Barry
> 
> 
> On Jan 18, 2014, at 5:59 PM, Dharmendar Reddy <dharmareddy84 at gmail.com> wrote:
> 
> > On Sat, Jan 18, 2014 at 3:54 PM, Karl Rupp <rupp at mcs.anl.gov> wrote:
> >> Hi,
> >>
> >>
> >>
> >>>                  I am solving a set of equations with SNES
> >>>
> >>> F1 (x1,x2,x3) = 0
> >>> F2 (x1,x2,x3) = 0
> >>> F3 (x1,x2,x3) = 0
> >>>
> >>> The system of equations is shown on page 1 of pdf here
> >>> http://dunham.ee.washington.edu/ee531/notes/SemiRev.pdf
> >>>
> >>> F1 = equation 1
> >>> F2 = equation 2
> >>> F3 = equation 5
> >>>
> >>> x1 = n, X2=p and X3 = psi,
> >>> X1 and X2 have an exponential dependance on X1
> >>> after i scale the variables, X3 typically varies between say +/- 100
> >>> where as X1 and X2 vary between 0 to 2. norm(X) then may usually
> >>> dominated by solution values of X3.
> >>
> >>
> >> If you are solving the drift-diffusion system for semiconductors, which
> >> discretization do you use? How did you stabilize the strong advection?
> >>
> >>
> >
> > My plan is to use the discretization method described here.
> > (http://www.iue.tuwien.ac.at/phd/triebl/node30.html ).
> >
> > The method typically used for for stabilizing the advection term is
> > called Scharfetter-Gummel method described the above link.
> >
> > When i intially started the code design, i wanted to implement the
> > approach mentioned  in this paper (dx.doi.org/10.2172/1020517) . I am
> > still learning about this things so..i am not sure which is the right
> > way to go.
> >
> > For stabilizing, i implemented the bank n rose algorithm via
> > SNESPostCheck, i am yet to test the efficacy of this method over the
> > defualt snes methods.
> > (http://www.iue.tuwien.ac.at/phd/ceric/node17.html)
> >
> >
> >
> >>
> >>> Can you suggest me the snes options that i need to use to achieve the
> >>> following:
> >>>
> >>> 1. X1 > 0 and X2 > 0  (as per previous emails, i can use
> >>> SNESSetVariableBounds)
> >>
> >>
> >> Have you considered a transformation to quasi-fermi potentials, i.e.
> >> n ~ exp(phi_n), p ~ exp(phi_p)
> >> or Slotboom variables? This way you could get rid of the constraint
> >> entirely. Even if you solve for (n,p,psi), my experience is that positivity
> >> is preserved automatically when using a good discretization and step size
> >> control.
> >>
> >>
> >>
> >>> 2. I want the updates to solution to have an adaptive stepping based
> >>> on norm of (F) or norm(X). If norm(F) is decreasing as the iteration
> >>> progresss, larger stepping others wise reduce the step size..
> >>> Similarly for Norm of X.
> >>
> >>
> >> A good damping for the drift-diffusion system is tricky. I know a couple of
> >> empirical expressions, but would be interested to know whether this can be
> >> handled in a more black-box manner as well.
> >>
> >> Best regards,
> >> Karli
> >>
> 
>