[petsc-users] Help using FAS as an initial guess

[Barry Smith]

  You might consider https://petsc.org/release/manualpages/SNES/SNESSetGridSequence/ it does exactly what I think you want to do.

  FAS is a bit more subtle than that. The "coarse grid problem" that FAS builds and solves are dependent on the current fine grid solution so you need an "approximate" fine grid solution already in order to create a FAS coarse problem. Of course FAS can, and often should, be used also with grid sequencing to boot-strap the fine grid solutions.

  Barry


> On May 2, 2023, at 5:40 PM, Takahashi, Tadanaga <tt73 at njit.edu> wrote:
> 
> Hi, 
> 
> I want to know how to configure the FAS so that it solves a problem on a coarse grid of size 4h, interpolate the solution, and then stop. 
> 
> Here is the context: I am using Newton LS to solve a problem on square domain discretized with DMDA meshed with step size h. I have a subroutine to compute the initial guess. I want this subroutine to first do a Newton solve on a coarse grid of size 4h. Then it interpolates the solution to the main mesh. I think this is achievable by using one iteration of FAS. Below is the gist of what my subroutine looks like: 
> 
> PetscErrorCode InitialState(DM da, Vec u) { // 
> SNES snes; 
> SNESCreate(PETSC_COMM_WORLD,&snes);  
> SNESSetDM(snes,da);
> SNESSetType(snes,SNESFAS); // solve with multigrid
> SNESSetTolerances(snes,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,1,PETSC_DEFAULT); // just one iteration
> VecSet(u,0.0);            // start with zeros 
> SNESSolve(snes,NULL,u);   // cheap solve 
> SNESGetSolution(snes,&u); // extract solution 
> }
> 
> For some reason, my initial guess is too accurate. The initial guess produced by this subroutine looks exactly like the final solution. My guess is that it's doing more than what I want it to do. I'm still new to FAS. How can I tell FAS to do just one crude solve and an interpolation?

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