> - Add a new enum SCALAR to FEFamily (or alternatively, a new enum SCALAR
> to Order)?

Something like that sounds good...  This is a single scalar value coupled to
*all* other DOFs?

> - Short circuit all the loops over elements for DOF counting in DofMap
> for SCALAR variables, and instead store the dof index of each SCALAR
> variable in a vector in DofMap?

I would think the DofMap needs to store a vector of scalar indices, yeah....

> - However, I can't see where in the code one should compute the dof
> index of a SCALAR variable in the first place?

Well, after the typical dof indexing each processor knows the local number
of Dofs and their global Dof indices, [0, n_global_dofs) so don't the
scalars get numbered sequentially in
 [n_global_dofs, n_global_dofs+n_scalars) ?

> - Ben, regarding setting the nonzero count and the number of rows that
> you mentioned; where is this controlled? In SparsityPattern?

Yeah, the sparsity pattern is constructed, potentially handed off to
initialize matrices, then the nonzeros are counted, and it is removed to
save storage.

Everything should fall through provided:

(1) DofMap::dof_indices() tacks on the scalar indices for an element when it
is called, since you are expecting them to be coupled to all elemend dofs,
and
(2) n_scalar additional, *full* rows are added at the end of the sparsity
pattern.

I think it would be pretty easy to code up and try in serial, not sure at
what point in parallel we will need to get smarter with the load balancing.
probably round-robbin'ing the scalars across processors is a better idea
than putting them continuously at the end, and thus in the last processor's
memory...

-Ben

So at the end of the sparsity pattern construction we a



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