[petsc-users] Nesting splits based on IS

[Karin&NiKo]

Dear Matt and Barry,

Unfortunately DM is not used in our PETSc interface,which is essentially
based on  the assembly matrix.
As Matt mentioned, the trick could be to define a DMShell in order to
expose the splits we internally build based on IS.
If I understand well, I have to play around with
DMShellSetCreateFieldDecomposition. Unfortunately, I do not find tests
using this method. Am I missing something ?
Perhaps a good starting point would be to write a test
like src/ksp/ksp/examples/tutorials/ex43.c in which one would consider the
algebraic data to be known (the matrix and the IS) and would set up a
DMShell  (with an appropriate call to DMShellSetCreateFieldDecomposition).
Does that make sense?

Thanks,
Nicolas

Le dim. 18 avr. 2021 à 15:54, Matthew Knepley <knepley at gmail.com> a écrit :

> 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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