Re: Nonlinear CG

One approach that we used with ITL that worked fairly well was a  
matrix-free Newton-Krylov approach (cf Brown and Hindmarsh).  I think  
ITL has example code for this in one of the subdirectories.

Cheers,
Andrew Lumsdaine

On Jan 12, 2007, at 11:42 AM, Peter Gottschling wrote:

> Hi Ben,
>
> I'm not an expert of non-linear solvers.  Most things I have seen  
> (a while ago) were approximated Newton schemes with Jacobi matrix  
> was approximated from the operator.  This requires (I think) that  
> one has a matrix representation of the operator which I'm afraid  
> you probably don't.
>
> Regarding pseudocode or free software I would need to search too.
>
> Best Regards,
> Peter
>
> On 09.01.2007, at 18:38, Ben FrantzDale wrote:
>
>> Peter,
>> Interesting. I'll start thinking about it.
>>
>> I think most nonlinear CG flavors require one additional concept:  
>> a function,
>>   func(const vector& x, scalar& result, vector& result_gradient),
>> which computes f(x) and f'(x).
>>
>> I actually don't want to use PETSc data. My state vector  
>> represents atom positions as well as continuum displacements,  
>> stored separately, so basically it's a heterogeneous mess. (This  
>> is part of the reason a generic approach seems so appealing – I  
>> should be able to abstract that heterogeneity away.)
>>
>> Do you know where I might find pseudocode (or just Free code) for  
>> of algorithm?
>>
>> —Ben
>>
>>
>> On 1/9/07, Peter Gottschling < [email protected]> wrote:Dear Ben,
>>>
>>> As far as I know, non-linear solvers does not exist in ITL.  It  
>>> is an
>>> excellent idea and we will likely work on it in the future.  If you
>>> want to work on this, I'd be happy to support you.
>>>
>>> I don't know if that helps you, I've written an interface between  
>>> PETSc
>>> and parallel BGL so that one can read out parallel PETSc matrices  
>>> from
>>> generic libraries and also access to distributed PETSc vector  
>>> without
>>> copying them.  However, it sounds more that you want to use PETSc  
>>> data
>>> with in a clearer way than I did. ;-)
>>>
>>> Best Regards,
>>> Peter
>>>
>>> On 09.01.2007, at 18:01, Ben FrantzDale wrote:
>>>
>>> > Dear ITL-devel,
>>> > I'm glad I finally found ITL. It looks like it could be the  
>>> Right Way
>>> > to solve a bunch of problems that various closed-source Fortran
>>> > libraries have attempted.
>>> >
>>> > I am interested in solving large nonlinear minimization  
>>> problems in
>>> > parallel. Presently we are experimenting with several CG  
>>> solvers. The
>>> > work, but all of them want to see the state vector as a single
>>> > contiguous array of doubles. The ITL example using PETSc in  
>>> parallel
>>> > makes me think there are interesting possibilities for large  
>>> nonlinear
>>> > problems as well.
>>> >
>>> > The ITL distribution includes two nonlinear examples, but all  
>>> of the
>>> > solvers appear to be linear. Has anyone extended ITL to do  
>>> nonlinear
>>> > minimization?
>>> >
>>> > Again, great work.
>>> >
>>> > Thanks,
>>> > Ben FrantzDale_______________________________________________
>>> > This list is archived at http://www.osl.iu.edu/MailArchives/mtl- 
>>> devel/
>>> ------------
>>> Peter Gottschling, Ph.D.
>>> Research Associate
>>> Open Systems Laboratory
>>> Indiana University
>>> 135 Lindley Hall
>>> Bloomington, IN 47405
>>> Tel.: +1-812-855-3608   Fax: +1-812-856-0853
>>> http://www.osl.iu.edu/~pgottsch
>>>
>>>
>>> _______________________________________________
>>> This list is archived at http://www.osl.iu.edu/MailArchives/mtl- 
>>> devel/
>> _______________________________________________
>> This list is archived at http://www.osl.iu.edu/MailArchives/mtl- 
>> devel/
> ------------
> Peter Gottschling
> Research Associate
> Open Systems Laboratory
> Indiana University
> 135 Lindley Hall
> Bloomington, IN 47405
> Tel.: +1-812-855-3608   Fax: +1-812-856-0853
> http://www.osl.iu.edu/~pgottsch
> _______________________________________________
> This list is archived at http://www.osl.iu.edu/MailArchives/mtl-devel/

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