[petsc-users] Tao iterations

[Justin Chang]

Ah I see that makes sense. Thank you very much

On Monday, June 8, 2015, Jed Brown <jed at jedbrown.org> wrote:

> Justin Chang <jychang48 at gmail.com <javascript:;>> writes:
>
> > Jed,
> >
> > Thank you for your response. I agree completely with all that you said. I
> > just wonder what would happen if I attempted to use the TAO routines
> after
> > forming the Jacobian J and residual r arising from the advection
> diffusion
> > equation.
> >
> > In my current (linear) diffusion framework, i have the following
> objective
> > function and gradient vector:
> >
> > f = \frac{1}{2} x \cdot J*x + x\cdot[r - J*x^(0)]
>
> If J is non-symmetric, then you're no longer looking for a minimum of
> this functional.  Let's take a prototypical example in 2 variables
>
>   J = [0 1; -1 0]
>
> Now the J-"inner product"
>
>   conj(x) \cdot J x = 0
>
> for all real-valued x.  (I'll assume you're working over the reals.)
> Similarly, the J-"inner product" with
>
>   J = [1 1; -1 1]
>
> is identical to that with J = eye(2), but obviously you want the
> anti-symmetric part to affect your solution.
>
> In short, none of this makes mathematical sense in the way you intend if
> J is nonsymmetric.
>
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