[petsc-dev] manual page for TSSetIJacobian()

[Barry Smith]

On Feb 7, 2011, at 3:47 PM, Jed Brown wrote:

> On Mon, Feb 7, 2011 at 22:19, Barry Smith <bsmith at mcs.anl.gov> wrote:
> It uses U0 but never explains what it is. It also calls a the "shift" but never explains what it is. Perhaps some notes explaining this stuff would make the solver more transparent. And a reference to further material that uses this approach would be great if it exists.
> 
> Suppose we have f(x,y). There are two ways to express the derivative we need
> 
> 1. f_x(x,y) + a*f_y(x,y)
> 2. g_x where g(x) = f(x,z+a*x)
> 
> I used version 2 in the man page because I think 1 looks arbitrary and is less obvious how it arises from a time integrator. There is a note later in the page about the equivalence. I suppose the name "shift" is more natural for version 1. Do you think I should make version 1 primary (or remove any mention of 2)?
> 
> Do you have a better name for "shift", or just want more text (I felt like elaborating would be describing a simple equation in words)?

  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?

   Barry