[dune-functions] Global Id of dune-function basis DOFs

[Christian Engwer]

Hi Simon,
the implementation would be simpler than you think...

>Since bases have different continuity properties, a purely generic
>implementation is not possible. So, one has to provide this continuity
>information for each basis in some way. On a local domain, the DOFs get
>a continuous or discontinuous index from the LocalView. But on
>distributed grids, this information is not given, currently.

No, the DOFs are associated with a particular (sub)entity and have a local per-entity index, trusted to the tree. You can use this for DG as well as for conforming spaces.

>Essentially what you need is some identification of the node in the
>tree
>+ the DOF id of a local basis on that node. So, some kind of tuple,
>e.g.
>for LagrangeDG
>
>(treePath, localDofId)
>
>where localDofId could be something like
>
>localDofId := (global-elementId, localDofIndex)

This is basically what I suggested and it works in any case... As the is is unique over all geometry types, this is the same id as your suggestion below.

>For continuous Lagrange DOFs it is a bit more delicate. For low order
>Lagrange, we can assume that there is <= 1 DOFs per entity and one
>could
>use something like
>
>localDofId := (global-entityId, localIndexOnEntity)
>
>where localIndexOnEntity==0 and the entity is extracted from the
>localKey.
>
>So, each basis node needs a different handling of the identification of
>DOFs.

Up to now this is _not_ the case. Also the mapping described below can be defined just by global information, but I agree, that we possibly want some right interface.

Christian

>For other bases than Lagrange, one might need additional information to
>make it continuous, like a global unique orientation of facets. Since
>we
>have ordered global entity ids this should be possible to provide.
>
>I don't know all bases in detail, so there might be a basis, where this
>global continuity information is harder to obtain.
>
>Either I define a functions/class GlobalDOFId that specialized for each
>PreBasis type and calculates the global id for a local DOF, or this can
>be added to the PreBasis implementation directly. (The first option is
>not so nice, since the PreBasis types change from dune-functions
>version
>to version. Currently I have to support the dune-functions 2.6 class
>signature and the 2.7 PreBasis type, and with some other MR in
>dune-functions this type changes again. So a simple specialization is a
>bit annoying)
>
>Best,
>Simon
>
>PS: there is a more complete sketch in the branch
>
>https://gitlab.dune-project.org/simon.praetorius/dune-functions/tree/feature/global_dof_ids
>
>where this global ID is implemented for Lagrange, LAgrangeDG, Power,
>Composite, and TaylorHood PreBases.
>
>>
>> The simplest way to generate a final I'd is to take the Multiindex
>and use the entity id instead of the geometryindex/entityindex pair.
>Alternatively one could just append the per-entity numbering to the
>entity-id (in the sense of a tuple).
>>
>> Ciao
>> Christian
>>
>>> For a LagrangeDG basis, one could think of a global id easily, e.g.
>the
>>> global element id + a local key of the local DOF. but for the
>>> continuous
>>> Lagrange basis it is already "slightly" more complicated, since the
>>> connectivity of multiple DOFs per entity can not easily be
>determined,
>>> without the help of some non dune-core functionality, like the
>>> TwistUtilities from dune-fem. Also, one can not distinguish the
>>> LagrangeNode and the LagrangeDGNode, since they are just aliases.
>So,
>>> it
>>> is difficult to specialize a user-defined function, based on the
>node
>>> type (that i receive when walking through the basis tree using
>>> forEachLeafNode, for example)
>>>
>>> A first thought was, that maybe one should extend the GlobalBasis
>with
>>> some kind of GlobalIdSet (similar to what is in the grid) that
>uniquely
>>> identifies the DOFs in a distributed grid. If this is in the basis,
>one
>>> does not need to walk through the nodes manually and write for each
>>> possible basis a wrapper function, but the writer of a basis has to
>>> think about a possible parallel global id for the DOFs.
>>>
>>> See also
>>>
>>>> https://gitlab.mn.tu-dresden.de/snippets/2
>>> for a sketch of the implementation.
>>>
>>> One probably should add a GlobalView next to LocalView or something
>>> similar to the GlobalBasis to initialize the global ids only when
>>> needed. (the names local and global have multiple meanings here,
>this
>>> should be clarified)
>>>
>>> Do you think this is a extension that could be implemented? Maybe it
>is
>>> not possible for all types of dune-function bases.
>>>
>>> Best wishes,
>>> Simon
>>>
>>>
>>>
>>>
>>> _______________________________________________
>>> dune-functions mailing list
>>> dune-functions at lists.dune-project.org
>>> https://lists.dune-project.org/mailman/listinfo/dune-functions