[petsc-users] Nesting splits based on IS

[Matthew Knepley]

On Sat, Apr 17, 2021 at 6:13 PM Barry Smith <bsmith at petsc.dev> wrote:

>
>   So you would like to be able to create three IS in your code and attach
> them with names to the PC.  Then have -pc_fieldsplit_XXX_fields be able to
> utilize the attached IS by name and use them to define the blocks.
>
>   This is all doable and could be added to PCFIELDSPLIT without too much
> code, new code. The code would be largely like
> PCFieldSplitSetRuntimeSplits_Private.
>
>    The recursive part may also be doable but I think your syntax below is
> not exactly right. You would need something like
>
> -fieldsplit_0_pc_type fieldsplit   // split the first PC into a fieldsplit
>      -fieldsplit_0_pc_fieldsplit_0_fields xxx
> -fieldsplit_0_fieldsplit_0_pc_type jacobi
>      -fieldsplit_0_pc_fieldsplit_1_fields yyy
>      etc
>
> this would split the first field into two fields and use jacobi on the
> first field.
>
> The problem is what to use for labelling the xxx and the yyy?
>
> I think one could achieve this by having the PCFIELDPLIT attach to each of
> its split PCs the appropriate modified IS with names attached to them.
> There are two cases,
>
>   when building the split uses first all the entries from fieldsplit_v_,
> then from fieldsplit_p_ then the new ISs it needs to attach to the first
> split PC are two sets of integers the first from 0 to the len(v)-1 and the
> second from len(v) to len(v)+len(p)-1.
>
>   when building the split it interlaces the indices from v and p
> (interlacing only make sense if the size of v and p is the same). Then the
> new v would be {0,2,4,...} and p would be {1,3,...}.
>
>   If you are ambitious and would like to add this to fieldsplit.c we'd be
> very happy to receive an MR. It might even lead to allowing us to simply
> how the PCFIELDPLIT interacts with DMs. If all the split type, stride,
> named, etc are handle in a single consistent manner.
>

Barry, this is already working with DMs, which I think is the right way to
do this.

Here is the code:


https://gitlab.com/petsc/petsc/-/blob/main/src/ksp/pc/impls/fieldsplit/fieldsplit.c#L420

The DM must respond to DMCreateSubDM(). The interface is that the call
provides a list of fields [f_0, f_1, ...]
and the DM returns an IS for that combination and a subdm for it. The subdm
part is what allows you to do this
recursively, since you make the same call on the subdm.

If you use a PetscSection to keep track of the data layout, the code to do
field selection is already done:

  https://gitlab.com/petsc/petsc/-/blob/main/src/dm/interface/dmi.c#L105

which can just be called from the DMCreateSubDM() implementation.

  Thanks,

     Matt


>   Barry
>
>
>
> > On Apr 17, 2021, at 11:53 AM, Karin&NiKo <niko.karin at gmail.com> wrote:
> >
> > Dear PETSc users,
> >
> > I use the fieldsplit PC in an application where the splits are
> programmatically defined by IS using PCFieldSplitSetIS. Then the user can
> specify its own PC at runtime using PETSc options.
> > My question : is it possible to define nested splits in this case as it
> can be done with strided splits (see snes/examples/tutorials/ex19.c with
> test suffix fieldsplit_4).
> >
> > In order to be perfectly clear : let's say I have a 3 fields problem :
> velocity (v split), pressure (p split) and temperature (t split).
> > What I would like to do is something like the following but it fails :
> >
> > -ksp_type fgmres
> > -pc_fieldsplit_type multiplicative
> > -pc_type fieldsplit    -pc_fieldsplit_0_fields fieldsplit_v_,
> fieldsplit_p_    -pc_fieldsplit_1_fields fieldsplit_t_
> >
> > -prefix_push  fieldsplit_0_
> > -ksp_type fgmres
> > -pc_fieldsplit_schur_factorization_type upper
> > -pc_type fieldsplit
> > -pc_fieldsplit_type schur
> > -pc_fieldsplit_schur_precondition a11
> > -prefix_pop
> >
> > -prefix_push  fieldsplit_1_
> > -ksp_type fgmres
> > -pc_type jacobi
> > -prefix_pop
> >
> > -prefix_push  fieldsplit_v_
> > -ksp_type fgmres
> > -pc_type gamg
> > -prefix_pop
> >
> > -prefix_push  fieldsplit_p_
> > -ksp_type fgmres
> > -pc_type jacobi
> > -prefix_pop
> >
> > I thank you for your help,
> > Nicolas
> >
> >
>
>

-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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