[petsc-users] SNES_DIVERGED_LS_FAILURE

[Juha Jäykkä]

> 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.

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.

Cheers,
-Juha

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