[petsc-users] SNES_DIVERGED_LS_FAILURE

[Matthew Knepley]

On Thu, Jun 23, 2011 at 6:13 AM, Juha Jäykkä <juhaj at iki.fi> wrote:

> > What physical system does it represent and what sort of discretization
> are
> > you using?
>
> Please see arXiv:0809.4303 for details. The equation is obtained from the
> Lagrangian (4) by imposing cylindrically symmetric u with z and t appearing
> in
> complex exponential in a certain way, which decouples z and t from the
> planar
> variables. Furthermore, the angular variable vanishes (the whole point of
> the
> ansatz), leaving one with just the equation for the radial profile of u.
> (This
> is all similar to what is done in the article at Eq. (17), but the article
> has
> further constraints imposed, which eventually gives exact solutions.)
>
> After some rescaling of the domain and the codomain, one ends up with
> unknown
> g:[0,1] -> [0,1], which is what I am solving.
>
> > Do you know that the equations have a solution for all values of the
> > parameter? Even simple problems may not have solutions for all values of
> a
>
> Given the origin of the equation - a well defined Hamiltonian/Lagrangian, I
> would be very surprised if there were no solutions. It is hard to prove,
> either way, though. If I treat the problem as 3D energy minimisation one, I
> do
> find solutions (of course I do: the energy is bouded from below!), which
> look
> very much like what the diverged SNES line searches end up with, but not
> quite. Therefore I believe there are solutions and end up with the theory I
> explained in the original post.
>
> Oh, now that the equations are there, the parameters I am scanning are the
> product \beta e^2 and n, where n is comparable to the n in Eq (17).
> Obviously,
> n is an integer so cannot be continued as such, but \beta e^2 is real, so I
> start with \beta e^2 = 1, n=1, where the solution is g(y) = y.
>

You could relax integrality.


> Which reminds me of another oddity: if I start with the exact solution, my
> function value is ~ 1e-11, so I know for sure to keep -snes_atol ~1e-10
> because that's the best my function evaluation can do. Could this be the
> problem? Too little accuracy in function? I did try up to 6th order central
> differences, but it does not help.
>

It is possible for the discrete equation to have no real solutions, while
the
continuous equation does. Even if it is expensive, I suggest continuing in
the
nonlinearity to try to get to a solution. If you find one, it could give you
insight
into designing a search strategy that will work for your equation.

   Matt


> Cheers,
> -Juha
>
> --
>                 -----------------------------------------------
>                | Juha Jäykkä, juhaj at iki.fi                     |
>                | http://www.maths.leeds.ac.uk/~juhaj           |
>                 -----------------------------------------------
>



-- 
What most experimenters take for granted before they begin their experiments
is infinitely more interesting than any results to which their experiments
lead.
-- Norbert Wiener
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