Marker-wise constant FE Space

[Lukas Korous]

Hello,

I would like to ask for help in implementing a special piece-wise constant FE space that has 1 constant basis function per a mesh (cell) marker.

The purpose is to calculate a total electric current induced in the area with the particular marker.

What would be the best way to implement something like that?

Thank you,

Lukas

[Daniel Arndt]

Lukas,

I am not entirely clear what you mean by mesh marker. In general finite element spaces are defined for each element.
It sounds that FE_DGQ(0) should be the right finite element for you as it provides one constant basis function per cell.
Using identity constraints you can then restrict your ansatz space to patchwise constant functions.

Best,
Daniel

[Lukas Korous]

Hi Daniel,

thank you - this is how we originally implemented it, but it is quite computationally intensive. If we only had a single constant basis function per patch, such a (very small) space would render the calculation much faster - we are interested in this. The question  is if deal.ii enables us to do this in any way - do you see a way?

Thank you,
Lukas

[Daniel Arndt]

Hi Lukas,

Unfortunately, I don't see a way on how to accomplish this by creating a new FE space.
It is somehow surprising that the approach with FE_DGQ(0) elements is computationally expensive for you.
I don't think that your suggestion would be much different.
May be you can tackle the problem from another side. What is the equation you want to solve using this ansatz space?

Best,
Daniel

[Lukas Korous]

Hi Daniel,

OK, thank you - the thing is that it is already a "full" problem to which we need to add just this calculation of total current, so solving  this "full" problem coupled with another "full" problem with FE_DGQ(0) space you describe together with a bunch of constraints will be quite intensive. The approach we used (the patchwise one) in another software was basically adding (n = # of patches) equations.

But then again solving the coupled problem deal.ii might be fast enough for us - I will give it a shot and report back.

Thanks,
Lukas