[petsc-users] fixed point interations

[Matthew Knepley]

On Sat, Nov 5, 2011 at 3:45 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote:

> On Sat, Nov 5, 2011 at 08:06, Matthew Knepley <knepley at gmail.com> wrote:
>
>> I want to start small by porting a very simple code using fixed point
>>> iterations as follows: A(x)x = b(x) is approximated as A(x0)x = b(x0),
>>> then solved by KSP for x, then x0 is updated to x, then repeat until
>>> convergence.
>>>
>>
> Run the usual "Newton" methods with A(x) in place of the true Jacobian.
> You can compute A(x) in the residual
>
> F(x) = A(x) x - b(x)
>
> and cache it in your user context, then pass it back when asked to compute
> the Jacobian.
>
> This runs your algorithm (often called Picard) in "defect correction
> mode", but once you write your equations this way, you can try Newton
> iteration using -snes_mf_operator.
>
>
>>
>>> In the documentation chapter 5 I see all sorts of sophisticated Newton
>>> type methods, requiring computation of the Jacobian. Is the above
>>> defined simple method still accessible somehow in Petsc or such
>>> triviality can only be done by hand? Which one from the existing
>>> nonlinear solvers would be a closest match both in simplicity and
>>> robustness (even if slow performance)?
>>>
>>
>> You want -snes_type nrichardson. All you need is to define the residual.
>>
>
> Matt, were the 1000 emails we exchanged over this last month not enough to
> prevent you from spreading misinformation under a different name?
>

Tell people whatever you want. The above is just Newton or "iterative
refinement" in thousands of NA papers.

  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
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