[petsc-users] How to use DM_BOUNDARY_GHOSTED for Dirichlet boundary conditions

[Barry Smith]

  I have not seen explicitly including, or excluding, the Dirichlet boundary values in the system having a significant affect on the convergence so long as you SCALE the diagonal rows (of those Dirichlet points) by a value similar to the other entries along the diagonal. If they are scaled completely differently, that can screw up the convergence. For src/ksp/ksp/ex45.c I see that the appropriate scaling is used (note the scaling should come from a finite element view of the discretization even if the discretization is finite differences as is done in ex45.c)

   Are you willing to share the two codes so we can take a look with experienced eyes to try to figure out the difference?

  Barry




> On Feb 27, 2023, at 5:48 PM, Paul Grosse-Bley <paul.grosse-bley at ziti.uni-heidelberg.de> wrote:
> 
> Hi Barry,
> 
> the reason why I wanted to change to ghost boundaries is that I was worrying about the effect of PCMGs coarsening on these boundary values.
> 
> As mentioned before, I am trying to reproduce results from the hpgmg-cuda benchmark (a modified version of it, e.g. using 2nd order instead of 4th etc.).
> I am trying to solve the Poisson equation -\nabla^2 u = 1 with u = 0 on the boundary with rtol=1e-9. While my MG solver implemented in hpgmg solves this in 40 V-cycles (I weakened it a lot by only doing smooths at the coarse level instead of CG). When I run the "same" MG solver built in PETSc on this problem, it starts out reducing the residual norm as fast or even faster for the first 20-30 iterations. But for the last order of magnitude in the residual norm it needs more than 300 V-cycles, i.e. it gets very slow. At this point I am pretty much out of ideas about what is the cause, especially since e.g. adding back cg at the coarsest level doesn't seem to change the number of iterations at all. Therefore I am suspecting the discretization to be the problem. HPGMG uses an even number of points per dimension (e.g. 256), while PCMG wants an odd number (e.g. 257). So I also tried adding another layer of boundary values for the discretization to effectively use only 254 points per dimension. This caused the solver to get even slightly worse.
> 
> So can the explicit boundary values screw with the coarsening, especially when they are not finite? Because with the problem as stated in ex45 with finite (i.e. non-zero) boundary values, the MG solver takes only 18 V-cycles.
> 
> Best,
> Paul
> 
> 
> 
> On Monday, February 27, 2023 18:17 CET, Barry Smith <bsmith at petsc.dev> wrote:
>  
>> 
>> Paul,
>> 
>> DM_BOUNDARY_GHOSTED would result in the extra ghost locations in the local vectors (obtained with DMCreateLocalVector() but they will not appear in the global vectors obtained with DMCreateGlobalVector(); perhaps this is the issue? Since they do not appear in the global vector they will not appear in the linear system so there will be no diagonal entries for you to set since those rows/columns do not exist in the linear system. In other words, using DM_BOUNDARY_GHOSTED is a way to avoid needing to put the Dirichlet values explicitly into the system being solved; DM_BOUNDARY_GHOSTED is generally more helpful for nonlinear systems than linear systems.
>> 
>> Barry
>> 
>> > On Feb 27, 2023, at 12:08 PM, Paul Grosse-Bley <paul.grosse-bley at ziti.uni-heidelberg.de> wrote:
>> >
>> > Hi,
>> >
>> > I would like to modify src/ksp/ksp/tutorials/ex45.c to implement Dirichlet boundary conditions using DM_BOUNDARY_GHOSTED instead of using DM_BOUNDARY_NONE and explicitly implementing the boundary by adding diagnonal-only rows.
>> >
>> > My assumption was that with DM_BOUNDARY_GHOSTED all vectors from that DM have the extra memory for the ghost entries and that I can basically use DMDAGetGhostCorners instead of DMDAGetCorners to access the array gotten via DMDAVecGetArray. But when I access (gxs, gys, gzs) = (-1,-1,-1) I get a segmentation fault. When looking at the implementation of DMDAVecGetArray it looked to me as if accessing (-1, -1, -1) should work as DMDAVecGetArray passes the ghost corners to VecGetArray3d which then adds the right offsets.
>> >
>> > I could not find any example using DM_BOUNDARY_GHOSTED and then actually accessing the ghost/boundary elements. Can I assume that they are set to zero for the solution vector, i.e. the u=0 on \del\Omega and I do not need to access them at all?
>> >
>> > Best,
>> > Paul Große-Bley
>>