[petsc-dev] Scatter a single local value to multiple global values

[Jed Brown]

Chris Eldred <chris.eldred at gmail.com> writes:

> Hey PETSc-dev,
>
> Is it possible to create a LocalToGlobal mapping (or another PETSc
> construct) such that a single local value is associated with multiple
> global values?
>
> For example, let's say I am in 1D with a DMDA with 4 elements using
> Ghosted boundaries.
> The global space looks like:
> 1 - 2 - 3 - 4
> and the local space looks like:
> 1 - 2 - 3 - 4 - 5 - 6
> and the default local to global mapping is:
> 0 -> -1
> 1 -> 0
> 2 -> 1
> 3 -> 2
> 4 -> 3
> 5 -> -1
> Can this be modified to something like:
> 0 -> -1
> 1 -> 0
> 2 -> 1
> 3 -> 2
> 4 -> 3 , 2
> 5 -> -1
> where now the value in index 4 of the local vector gets scattered to
> both index 2 and 3 in the global vector when using VecScatter with the
> LocalToGlobal mapping set to the above?
>
> What about when using MatSetValuesLocal? Is it possible to have a
> single entry in the local matrix get put into multiple locations in
> the global matrix? When the row and column LocalToGlobal maps are
> different?
>
> If so, are there any example or writeups of how to do either of these?

No, you can have different local indices map to the same global index,
but you can't have one local index map to multiple global indices.  If
such a semantic were supported, what would the result of a
Global-to-Local update even mean?

> It's seems like star forests are the way to do this, but I don't
> really understand how they work. Is there a writeup for them?

Slightly dated, but mostly accurate.

https://jedbrown.org/files/StarForest.pdf

In SF terminology, you can't have a leaf map to multiple roots.

> The context for this question is a multipatch finite element code,
> where each patch is treated using a DMDA and we would like to couple
> degrees of freedom along patch boundaries, such that when the
> contribution of the elements along a boundary to the global matrix are
> computed the result goes into the rows for the dofs on each patch (and
> similarly for residual calculations).

That's a good way to produce a singular global matrix.  Either eliminate
the duplicated degrees of freedom (this is the standard method, slave
dofs are written as a linear combination of master dofs) or introduce a
Lagrange multiplier to enforce continuity.
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