Yuyun,
If you are speaking about using a finite difference stencil on a structured
grid where you provide the Jacobian vector products yourself by looping over
the grid doing the stencil operation we unfortunately do not have exactly that
kind of example.
But it is actually not difficult. I suggest starting with
src/ts/examples/tests/ex22.c It computes the sparse matrix explicitly with
FormIJacobian()
What you need to do is instead in main() use MatCreateShell() and
MatShellSetOperation(,MATOP_MULT,(void (*)(void))MyMatMult) then provide the
routine MyMatMult() to do your stencil based matrix free product; note that you
can create this new routine by taking the structure of IFunction() and
reorganizing it to do the Jacobian product instead. You will need to get the
information about the shell matrix size on each process by calling
DMDAGetCorners().
You will then remove the explicit computation of the Jacobian, and also
remove the Event stuff since you don't need it.
Extending to 2 and 3d is straight forward.
Any questions let us know.
Barry
If you like this would make a great merge request with your code to improve
our examples.
> On Feb 15, 2020, at 9:42 PM, Yuyun Yang <[email protected]> wrote:
>
> Hello team,
>
> I wanted to apply the Krylov subspace method to a matrix-free implementation
> of a stencil, such that the iterative method acts on the operation without
> ever constructing the matrix explicitly (for example, when doing backward
> Euler).
>
> I'm not sure whether there is already an example for that somewhere. If so,
> could you point me to a relevant example?
>
> Thank you!
>
> Best regards,
> Yuyun
