[petsc-dev] How do you get RIchardson?

[Matthew Knepley]

On Fri, Sep 16, 2011 at 5:02 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote:

> On Fri, Sep 16, 2011 at 23:54, Matthew Knepley <knepley at gmail.com> wrote:
>
>> On Fri, Sep 16, 2011 at 4:38 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote:
>>
>>> On Fri, Sep 16, 2011 at 23:21, Matthew Knepley <knepley at gmail.com>wrote:
>>>
>>>> it still converges, conditionally to the same solution as exact
>>>>> newton. Variations for A yield different rates of convergence. When
>>>>> A=1, you get the classical Picard iteration that Matt mentioned (?).
>>>>>
>>>>
>>>> Not even close.
>>>>
>>>
>>> From Barry's description at the top of this thread:
>>>
>>>  x^{n+1}   = x^{n}  - lambda F(x^{n})
>>>
>>>
>>> This looks oddly similar to
>>>
>>>  x^{n+1}   = x^{n}  - J(x^n)^{-1} F(x^{n})
>>>
>>> I wonder where I've seen that before.
>>>
>>
>> So you are saying that you agree with me, what is coded is in fact the
>> Picard iteration, and we are done arguing?
>
>
> I was objecting to your "not even close". I agree with Vijay's terminology.
>
> I agree that your choice is _a_ Picard iteration, I do not agree that it is
> the One True Picard iteration. In particular, it is not the one that is most
> commonly used in practice (e.g. SISC or JCP publications).
>
> Since Newton is also a fixed point iteration, I do not think the name
> "Picard" is a useful way to distinguish. Furthermore, since "Picard with
> solve" as you like to call it can easily be formulated in defect-correction
> mode as a Newton-like update with a different "Jacobian", it doesn't require
> any special support from PETSc.
>

So, you can accomodate your "Picard" iteration as Newton, but we cannot
accomodate the Picard iteration for
a system of nonlinear equations with that. So I made a class, named Picard,
to accomodate it. Are you really
still arguing about this?

   Matt

-- 
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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-dev/attachments/20110916/a70e8ef1/attachment.html>