[petsc-users] Matrix-free method in PETSc

[Smith, Barry F.]

  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 <yyang85 at stanford.edu> 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