[dune-pdelab] Grid operator for subspace?

[Gregor Corbin]

Hi Steffen,

thanks for the quick reply.

The reason why I never thought about splitting the spaces was that there
exists another update step, that updates both U and W at the same time.
On the other hand, due to restrictions in the interface of local
operators, I implemented this  step using low-level functions(bind,
read, ...), so I might as well split the function spaces as you suggested.

I currently do not use the Dirichlet constraints for W but assemble a
mass matrix for W as well( hence my earlier question about combined L2
operators).  Would Dirichlet constraints allow me to skip the mass
matrix assembly for W?


Concerning my second point: When I split all the function spaces, I wont
need a generalized L2 local operator any more. But maybe its is still a
useful addition to the codebase.

Is there a tutorial for TypeTree? It seems like a really useful tool,
not only for the PDELab context, so I would like to understand it
better.  What I currently know about it, I learned from browsing the
code, but at some point this gets a bit tedious.


Thanks for your help,

Gregor


Am 13.02.2018 um 13:56 schrieb Steffen Müthing:
> Hi Gregor,
>
>> Am 12.02.2018 um 18:22 schrieb Gregor Corbin <corbin at mathematik.uni-kl.de>:
>>
>> Hi everyone,
>>
>> I was wondering if one could define a grid operator that only updates
>> part of a CompositeGridFunctionSpace? In more detail, I have a
>> CompositeGridFunctionSpace of two Power-Spaces U and W.  One local
>> operator reads both U and W, but only contributes to the residual of U
>> and leaves W unchanged. Is there some way to tell the OneStepMethod that
>> W is constant to improve performance?
> there are a few points here:
>
> - You can of course write a LocalOperator that only updates part of a GFS. As the
>   GridOperator works additively, there just won’t be any change to the output for the
>   DOFs if you never call accumulate() for those DOFs.
>
> - I’m not quite sure what you are trying to do here (operator splitting?). If you never
>   need to write to both U and W in a single LocalOperator, it might be better to keep
>   the two spaces separate and provide W and its solution vector (or a grid function
>   that bundles the two) as a member function to the LocalOperator.
>
> - If you really want to keep the single global space, that will have one large solution
>   vector (and one large matrix for implicit methods), so apart from reduced assembly
>   work, there isn’t really a way to speed up the OneStepMethod if you don’t split the
>   spaces as suggested above. In this case, you also have to make sure to use Dirichlet
>   constraints on the whole subspace W - otherwise, the diagonal matrix block that
>   corresponds to the W subspace will be 0 and your matrix becomes singular.
>
>> Also, on a related note,  I had to write a local operator for the time
>> operator that basically applies the PowerL2 operator to U and W
>> separately. This only works so far for the functions space as above.
>> Since there will be more generalizations to my code at a later stage, I
>> wondered if there maybe is a L2 operator that works for general trees of
>> function spaces? If not, I suppose I could write one, but if it is not
>> necessary, I have no desire to enter that rabbit hole…
> - No, that doesn’t exist right now. Doing so requires a little bit of messing around with
>   TypeTree visitors. It’s actually not a lot of lines of code if you know what to do, I’ll write
>   one and open a MR.
>
> Cheers
> Steffen
>
>> Cheers,
>>
>> Gregor
>>
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