[petsc-dev] manual page for TSSetIJacobian()

Jed Brown jed at 59A2.org
Mon Feb 7 17:19:30 CST 2011


On Mon, Feb 7, 2011 at 23:52, Barry Smith <bsmith at mcs.anl.gov> wrote:

> On Feb 7, 2011, at 4:46 PM, Jed Brown wrote:
> > On Mon, Feb 7, 2011 at 23:35, Barry Smith <bsmith at mcs.anl.gov> wrote:
> > Well what I want is why is this "the derivative we need"? There is no
> hint as to an explanation why the user providing this quantity has any
> meaning a all. You could just as easily say g_x where g(x) = f(x, a*x^3 +
> 94) and why would that be wrong, while what you write is correct?
> >
> > That is the reason why I like introducing g(x) = f(x,xdot)
> > " where xdot is approximated by the integrator as z+a*x for some a and z
> depending on the integration method, step size, and past states."
>  This is exactly the kind of text I want.
> > But perhaps the user (as opposed to someone implementing a new TS)
> doesn't care at all and would be happy to evaluate f_x + a*f_xdot without
> any knowledge of why this beast is relevant.
>    The problem is not that you are providing too much information and
> should take some away. The problem is you are not providing enough. Just
> writing G(U) = F(t,U,U0+a*U) is not enough, you need to explain as you have
> above in your sentence that the schemes DO approximate xdot in that manner
> and therefor the Jacobian needed by the schemes is given by dF/dU +
> a*dF/dU_t
>   Barry
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