[petsc-users] -snes_type test shows differences

(Rebecca) Xuefei YUAN xy2102 at columbia.edu
Wed Feb 10 14:48:57 CST 2010

Dear Jed,

What if my F has the form(the full version):

F(f) = fxx+fyy+fxx*fyy-fxy*fxy-g = 0,

how should my Newton iteration look like?

J(f)h = -F(f) = -(fxx+fyy+fxx*hyy+fyy*hxx-fxy*hxy-fxy*hxy-g)?

I know h is the update, but what are hxx,hyy?

Any more references on this?

Thanks a lot!


Quoting Jed Brown <jed at 59A2.org>:

> On Wed, 10 Feb 2010 15:35:14 -0500, "(Rebecca) Xuefei YUAN"   
> <xy2102 at columbia.edu> wrote:
>> Hi,all,
>> I was writing analytic Jacobian to my FormJacobian(). However, I found
>> that there are quite big differences between finite difference
>> Jacobian and hand coded Jacobian. To simply the problem, assume that I
>> am solving a very simple equation as the residual function has the
>> form of
>> F = fxx*fyy - g.
>> Where f is the unknown, g is the given r.h.s.
> It looks like you have coded the Picard linearization.  You want the
> Newton linearization
>   J(f)h = fxx*hyy + hxx*fyy
> Jed

(Rebecca) Xuefei YUAN
Department of Applied Physics and Applied Mathematics
Columbia University

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