[petsc-users] Divergence when using Line Search

[Jed Brown]

On Tue, May 15, 2012 at 4:41 PM, Avery Bingham <avery.bingham at gmail.com>wrote:

> By scaling, I mean to say that a problem is poorly scaled if a change in x
> in a certain direction produces a much larger variation in f(x) than a
> change in another direction.  For a simple example is the scalar function:
> f(x) = 10^10*x1^2+x2^2
>

This is ill-conditioned, it just happens to be diagonal.


> A more practical example would be a physical coupled problem that has
> Pressure in ~10^6 Pascals and temperature in degrees ~100 C.
>

So if you have an accurate linear solve, this kind of ill-conditioning
should be taken care of (provided you are not up against finite precision).
If you can't do an accurate linear solve, or if you define the matrix by
finite differencing, then it's very important to fix the scaling in problem
formulation, otherwise you will constantly struggle with artificially
inaccurate finite differences and tricky convergence tolerances (the
residual is a poor indicator of convergence, etc).


>
>
>
>
> On Tue, May 15, 2012 at 3:45 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote:
>
>> On Tue, May 15, 2012 at 3:32 PM, Avery Bingham <avery.bingham at gmail.com>wrote:
>>
>>> I have also seen this behavior, and I think this might be related to the scaling of the variables in the nonlinear system.  I am using PETSc through an application of MOOSE which allows for scaling of the variables.  This scaling reduces the chance that the default cubic backtracking line search fails, but it is not reliable on all problems. Would it be possible to get a scaling-independent Line Search Method implemented within PETSc?
>>>
>>>
>> I'm not sure what you mean by scaling, but there is -snes_linesearch_type
>> cp (critical point) that might be useful.
>>
>
>
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