[petsc-users] fixed point interations

Jed Brown jedbrown at mcs.anl.gov
Sat Nov 5 10:45:25 CDT 2011


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?
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